Bibliography of the Duluth Summer Research Programs
1977 - 2024

under the supervision of Joseph A. Gallian

* denotes graduate student
** denotes PhD

1977 - Funded by NSF

Student Participants: David Housman and David Rusin.

David Rusin, What is the probability that two elements of a finite group commute? Pacific Journal of Mathematics , 82 (1979) 237-247.
Joseph A. Gallian and David Rusin, Factoring groups of integers modulo n,, Mathematics Magazine, 53 (1980) 33-36.
Joseph A. Gallian and David Rusin, Cyclotomic polynomials and nonstandard dice, Discrete Mathematics, 27 (1979) 245-259.
David Housman, Enumeration of hamiltonian paths in Cayley diagrams, Aequationes Mathematicae, 23 (1981) 80-97.

1978 - No Program

1979 - Funded by NSF

Student Participants: Judy L. Smith, Jeremy Teitelbaum, and David Witte.

David Witte, On hamiltonian circuits in Cayley diagrams, Discrete Mathematics, 38 (1982) 99-108.
Judy Smith and Joseph A. Gallian, Factoring finite factor rings, Mathematics Magazine, 58 (1985) 93-95.

1980 - Funded by NSF/UMD

Student Participants: Stephen Curran, Kevin Keating, Gail Letzter, and David Witte.

Stephen Curran and David Witte, Hamiltonian paths in cartesian products of directed cycles, Annals of Discrete Mathematics, 27 (1985) 35-74.
Kevin Keating, The conjunction of Cayley digraphs, Discrete Mathematics, 42 (1982) 209-219.
Gail Letzter, Hamiltonian circuits in cartesian products with a metacyclic factor, Annals of Discrete Mathematics, 27 (1985) 103-114.
David Witte, Gail Letzter, and Joseph A. Gallian, On hamiltonian circuits in cartesian products of Cayley digraphs, Discrete Mathematics, 43 (1983) 297-307.

1981 - Funded by NSF/UMD

Student Participants: Daniel Goldstein, Kevin Keating, Irwin Jungreis, Lawrence Penn, David Witte*

Irwin Jungreis, Infinite Hamiltonian paths in Cayley digraphs, Discrete Mathematics, 54 (1985) 167-180.
Kevin Keating, Multiple-ply hamiltonian graphs and digraphs, Annals of Discrete Mathematics, 27 (1985) 81-88.
Lawrence Penn and David Witte, When the cartesian product of two directed cycles is hypohamiltonian, Journal of Graph Theory 7 (1983) 441-443.

1982 - Funded by UMD

Student Participants: Stephen Curran, Kevin Keating, Richard Stong and David Witte*.

Kevin Keating and David Witte, On hamiltonian cycles in Cayley graphs in groups with cyclic commutator subgroup, Annals of Discrete Mathematics, 27 (1985) 89-102.
Richard Stong, On 1-factorizability of Cayley graphs, Journal of Combinatorial Theory, Series B, 39 (1985) 298-307.
Richard Stong, On hamiltonian cycles in Cayley graphs of wreath products, Discrete Mathematics, 67 (1987) 75-80.

1983 - Funded by UMD

Student Participants: David Witte*

David Witte and Joseph A. Gallian, A survey: Hamiltonian cycles in Cayley graphs, Discrete Mathematics, 51 (1984) 293-304.
Joseph A. Gallian and David Witte, Hamiltonian checkerboards, Mathematics Magazine, 57 (1984) 291-294.

1984 - Funded by UMD

Student Participants: David Witte*

David Witte, Cayley digraphs of prime-power order are hamiltonian, Journal of Combinatorial Theory, Series B, 40 (1986) 107-112.

1985 - Funded by NSF/UMD

Student Participants: Erich Friedman, Daniel Johnson, Douglas Jungreis.
Other Participants: Dr. Douglas Dunham and Dr. David Witte.

Joseph A. Gallian and David Witte, When the Cartesian product of two directed cycles is hyperhamiltonian, Journal of Graph Theory, 11 (1987) 21-24.
Joseph A. Gallian and Douglas S. Jungreis, Homomorphisms from Z_n[i] into Z_m[i] and Z_n[r] into Z_m[r] where i² + 1 = 0 and r² + r - 1 = 0, American Mathematical Monthly, 95 (1988) 247-249.
Douglas S. Jungreis, Generalized Hamiltonian circuits in the cartesian product of two directed cycles, Journal of Graph Theory, 12 (1988) 113-120.
Douglas S. Jungreis, Hamiltonian paths in Cayley digraphs of finitely-generated infinite abelian groups, Discrete Mathematics, 78 (1989) 95-104.
Douglas Dunham, Douglas S. Jungreis, and David Witte, Infinite Hamiltonian paths in Cayley digraphs of hyperbolic symmetry groups, Discrete Mathematics, 143 (1995) 1-30.
Douglas S. Jungreis and Erich Friedman, How many bridge auctions, The College Mathematics Journal, 19 (1988) 171-172.

1986 - Funded by NSF/UMD

Student Participants: Douglas Jungreis, Michael Reid, Daniel Ropp.
Other Participants: Dr. Douglas Dunham and Dr. David Witte.

Michael Reid, Douglas Jungreis, and David Witte, Distances forbidden by some two-coloring of Q², Discrete Mathematics, 82 (1990) 53-56.
Daniel Ropp, Graceful labelings of cycles and prisms with pendent points, Congressus Numerantium, 75 (1990) 218-234.
Joseph A. Gallian and Douglas Jungreis, Labeling books, Scientia, 1 (1988) 53-57.
Douglas Jungreis and Michael Reid, Labeling grids, Ars Combinatoria, 34 (1992) 167-182.

1987 - Funded by NSF/UMD

Student Participants: Robert Beals, Douglas Jungreis, David Moulton, Anne Wilkinson.
Other Participants: Dr. David Witte, Kevin Keating.

Dave Witte Morris, Joy Morris and David P. Moulton, Flows that are sums of hamiltonian cycles in abelian Cayley graphs, Discrete Mathematics, 299 (2005) 208--268.
David Moulton, Graceful labelings of triangular snakes, Ars Combinatoria, 28 (1989) 3-13.
Anne Marie Wilkinson, Circuits in Cayley digraphs of finite Abelian groups, Journal of Graph Theory, 14 (1990) 111-116.

1988 - Funded by NSF/NSA/UMD

Student Participants: Patrick Headley, Robert Hochberg, Sheri Jordan, Douglas Jungreis*, Bjorn Poonen, Michael Reid.

Robert Beals, Joseph A. Gallian, Patrick Headley, Douglas Jungreis, Harmonious groups, Journal of Combinatorial Theory, Series A, 56 (1991) 223-238.
David Moews, Pebbling graphs, Journal of Combinatorial Theory, Series B, 55 (1992) 244-252.
Bjorn Poonen, Union-closed families, Journal of Combinatorial Theory, Series A, 59 (1992) 253-268.
Patrick Headley, R-sequenceability and R*-sequenceability Abelian 2-groups, Discrete Mathematics, 131 (1994) 345-350.
Michael Reid, On the connectedness of unit distance graphs, Graphs and Combinatorics, 12 (1996) 295-303.

1989 - Funded by NSF/NSA/UMD

Student Participants: Stephen Bard, Douglas Jungreis*, Thomas Haines, David Moews, David Moulton, Matthew Mullin, Nikolai Weaver, Elizabeth Wilmer.
Other Participants: Dr. David Witte, Mike Reid*

Joseph A. Gallian and David Moulton, Classification of minimal non-prime power order groups, Archiv der Mathematik, 59 (1992) 521-524.
David Moews, Keller's conjecture for certain finite groups, Journal of Algebra, 142 (1991), 435-440.
Joseph A. Gallian and Matthew Mullin, Groups with anti-symmetric mappings, Archiv der Mathematik, 65 (1995) 273-280.
Elizabeth Wilmer (with Michael Ernst), Graphs induced by Gray codes, Discrete Mathematics , 257 (2002) 585-598.

1990 - Funded by NSF/NSA/UMD

Student Participants: Timothy Chow, David Moews*, David Moulton*, Matthew Mullin, Raymond Sidney, Eric Wepsic, Elizabeth Wilmer.
Visitor: Mike Reid*

Timothy Chow, Distances forbidden by two-colorings of Q³ and A_n, Discrete Mathematics, 115 (1993) 95-102.
Timothy Chow, Penny packing with minimal second moments, Combinatorica, 15 (1995) 151-158.

1991 - Funded by NSF/NSA/UMD

Student Participants: David Carlton, Jordan Ellenberg, Jason Fulman, David Moews*, David Moulton*, Michael Reid*, Zvezdelina Stankova, Virginia Wright, Jared Wunsch.

Zvezdelina E. Stankova, Forbidden subsequences, Discrete Mathematics, 132 (1994) 291-316.
Jason Fulman (with Denis Hanson and Gary MacGillivray), Vertex domination-critical graphs, Networks, 25 (1995) 41-43.
Jason Fulman, A note on the characterization of domination perfect graphs, Journal of Graph Theory, 17 (1993) 47-51.
Jason Fulman, A generalization of Vizing's theorem on domination, Discrete Mathematics, 126 (1994) 403-406.
Jared Wunsch, The Shields-Harary number for wheel and broken wheel graphs, Discrete Applied Mathematics, 59 (1995) 193-199.

1992 - Funded by NSF/NSA/UMD

Student Participants: Aaron Abrams, Susan Goldstine, David Moulton*, Catherine O'Neil, Matteo Paris, Lawren Smithline, Zvezdelina Stankova.
Visitors: Doug Jungreis**, Eric Wepsic.

Aaron Abrams, The k th upper chromatic number of the line, Discrete Mathematics, 169 (1997) 157-162.
Catherine O'Neil, Connectivity of n-tuple vertex graphs, Journal of Combinatorics, Information and System Sciences, 20 (1995) 153-159.
Matteo Paris, A note on the diameter of edge domination critical graphs, Networks, 24 (1994) 261-262.
Lawren Smithline, Bandwidth of the complete k-ary tree is known, Discrete Mathematics, 142 (1995) 203-212.
Zvezdelina E. Stankova, Forbidden subsequences of length 4, European Journal of Combinatorics, 17 (1996) 501-517.

1993 - Funded by NSF/NSA/UMD

Student Participants: David Dorrough, Leslie Hayes, Patricia Hersh, Daniel Isaksen, David Moulton*, Scott Nudelman, Michael Reid*, Jeffrey Vanderkam.
Visitors: Jason Fulman, Douglas Jungreis**, Kevin Keating**, Cathy O'Neil, Matteo Paris, David Witte**.

David Dorrough, Iterated triangular line graphs, Discrete Mathematics, 161 (1996) 79-86.
Scott Nudelman, The modular n-queens problem in higher dimensions, Discrete Mathematics, 146 (1995) 159-167.
Jeffrey Vanderkam, Path-sequential labelling of cycles, Discrete Mathematics, 162 (1996) 239-249.
Patricia Hersh, Exact n-step domination graphs, Discrete Mathematics , 205 (1999) 235-239.

1994 - Funded by NSF/NSA/UMD

Student Participants: Ruth Britto-Pacumio, Dean Chung, Daniel Isaksen*, Kiran Kedlaya, David Moulton*, Lenny Ng, Dana Pascovici, Jessica Wachter
Visitors: Tim Chow, Steve Curran, David Dorrough, Doug Jungreis**, Scott Nudelman, Matteo Paris, Lawren Smithline

Ruth Britto-Pacumio, Limits of iterated sequences of H- and S- line graphs, Discrete Mathematics, 199 (1999) 1-10.
Daniel Isaksen and David Moulton, Randomly planar graphs, Discrete Mathematics, 175 (1997) 265-269.
Kiran Kedlaya, Large product-free subsets of groups, Journal of Combinatorial Theory, Series A, 77 (1997) 339-343.
Kiran Kedlaya, Outerplanar partitions of planar graphs, Journal of Combinatorial Theory, Series B, 67 (1996) 238-248.
Lenny Ng and Michelle Schultz, On k-ordered Hamiltonian graphs, Journal of Graph Theory, 24 (1997) 45-57.
Dana Pascovici, On the forced unilaterial orientation number of a graph, Discrete Mathematics, 187 (1998) 171-183.

1995 - Funded by NSF/NSA/UMD

Student Participants: Manjul Bhargava, Ruth Britto-Pacumio, Daniel Isaksen*, Madeeha Khalid, Paul Li, Akira Negi, Lenny Ng, Ryan Siders
Visitors: David Moulton (research adviser)**, Tim Chow, Dean Chung, Fan Chung**, Danny Goldstein**, Ron Graham**, David Witte**

Manjul Bhargava, P-orderings and polynomial functions from arbitrary subsets of Dedekind rings, Journal fur die reine und angewandte Mathematik , 490 (1997) 101-127.
Manjul Bhargava, Congruence preservation and polynomial functions from Z_n to Z_m, Discrete Mathematics, 173 (1997) 15-21.
Manjul Bhargava, Generalized factorials and fixed divisors over subsets of a Dedekind domain, Journal of Number Theory, 72 (1998) 67-75.
Manjul Bhargava, The factorial function and generalizations, The American Mathematical Monthly, 107 (9) (200) 783-799.
Paul Li, Sequencing the dihedral groups D_4k, Discrete Mathematics, 175 (1997) 271-276.
Lenny Ng, Hamiltonian decomposition of complete regular multipartite digraphs, Discrete Mathematics, 177 (1997) 279-285.
Lenny Ng, Hamiltonian decompositions of lexicographic products of digraphs, Journal of Combinatorial Theory, Series B, 73 (1998) 119-129.

1996 - Funded by NSF/NSA/UMD

Student Participants: Daniel Biss, Tara Holm, Cameron Parker, Scott Sheffield, Sarah Spence, Julianna Tymoczko, Jonathan Weinstein.
Research advisers: David Moulton **, Daniel Isaksen*
Visitors: Manjul Bhargava*, Tim Chow, Kiran Kedlaya*, Lenny Ng*, David Witte**

Daniel Biss, A Presentation for un_n(F₂), Communications in Algebra, 26 (1998) 2971-2975.
Daniel Biss, A lower bound on the number of functions satisfying the strict avalanche criterion, Discrete Mathematics , 185 (1998) 29-39.
Tara Holm, On majority domination in graphs, Discrete Mathematics, 239 (2001) 1-12.
Kiran Kedlaya, Urn sampling and a majorization inequality, Journal of Combinatorial Theory, Series A, 79 (1997) 173-179.
Sarah Spence, Stratified graphs and distance graphs, Ars Combinatoria, 55 (2000) 233-246.
Ira Gessel, Jonathan Weinstein, and Herbert Wilf, Lattice walks in Z^d and permutations with no long increasing subsequences, The Electronic Journal of Combinatorics, 5 (1998), #R2, 11 pages.

1997 - Funded by NSF/NSA/UMD

Student Participants: Aaron Archer, Daniel Biss, Samit Dasguta, Ioana Dumitriu, Johanna Miller, Ronald Fertig,
Lauren Williams, Stephen Wang
Research adviser: Daniel Biss
Visitors: Brian Alspach**, Manjul Bhargava*, Daniel Biss, Tricia Hersh*, Tara Holm*, Daniel Isaksen*, Kevin Keating**, Kiran Kedlaya*, David Moulton**, Lenny Ng*, Lawren Smithline*, David Witte.

Aaron F. Archer, On the upper chromatic numbers of the reals, Discrete Mathematics, 214 (2000) 65-75.
Daniel Biss, Hamiltonian decompositions of recursive circulant graphs, Discrete Mathematics, 214 (2000) 89-99
Ioana Dumitriu, On generalized tribonacci sequences and additive partitions, Discrete Mathematics, 219 (2000) 65-83.
Samit Dasgupta, On the size of minimum super Arrovian domains, SIAM J. Discrete Mathematics, 12 (1999) 524-534.
Ron Fertig, On path-sequential labellings of cycles, Discrete Mathematics, 215 (2000) 21-32.
Stephen Wang, Pebbling and Graham's conjecture, Discrete Mathematics, 226 (2001) 431-438.
Lauren K. Williams, On exact n-step domination, Ars Combinatoria, 58 (2001) 13-22.

1998 - Funded by NSF/NSA/UMD

Student Participants: Michael Brewer, Michael Develin, Celeste Elton, Marci Gambrell, Stephen Hartke, Davesh Maulik
Research advisers: Daniel Biss*, Samit Dasgupta
Visitors: Aaron Archer*, Manjul Bhargava*, Ron Fertig, Tara Holm*, Daniel Isaksen*, Kiran Kedlaya*, David Moulton**,
Lenny Ng*, Dana Pascovici*, Lawren Smithline*, Zsuzsanna Szaniszlo**, Jonathan Weinstein*, Lauren Williams, David Witte.

Daniel K. Biss and Samit Dasgupta, A presentation for the unipotent group over rings with identity, Journal of Algebra, 237 (2001) 691-707.
Mike Develin, Avoidable sets in groups, Ars Combinatoria, 65 (2002) 279-297.
Mike Develin, A complete categorization of when generalized Tribonacci sequences can be avoided by additive partitions, The Electronic Journal of Combinatorics, 7 (2000) #R53, 7 pages
Marci J. Gambrell, Vertex-neighbor-integrity of expanders, magnifiers and hypercubes, Discrete Mathematics, 216 (2000) 257-266.
Stephen G. Hartke, Binary De Bruijn cycles under different equivalence relations, Discrete Mathematics, 215 (2000) 93-102.
Davesh Maulik, Root sets of polynomials modulo prime powers, Journal of Combinatorial Theory A, 93 (2001) 125-140.
. Samit Dasgupta, Gyula Karolyi, Balazs Szegedy, and Oriol Serra, On Additive Latin Transversals, Israel Journal of Mathematics, 126 (2001) 17-28.

1999 - Funded by NSF/NSA/UMD

Student Participants: Michael Develin (research adviser), Anna Draganova, Irina Goia, Daniel Johnston,
Matt Riddle, Beth Robinson, Cammie Smith, Joshua VonKorff
Research advisors: Daniel Biss*, Samit Dasgupta
Visitors: Aaron Archer*, Ron Fertig, Marci Gambrell, Stephen Hartke, Tricia Hersh, Davesh Maulik,
Daniel Isaksen*, David Moulton**, Lauren Williams, Elizabeth Wilmer**, David Witte**.

Mike Develin, On optimal subset representations of integers sets, Journal of Number Theory, 89 (2001) 212-221.
Anna Draganova (with M. Sutton and M. Miller), The mod sum number of the wheel W_n, Ars Combinatoria, 63 (2002) 273-287.
Anna Draganova, Results on F-continuous graphs, Czechoslovak Mathematical Journal, 59 (1), (2009) 51-60.
Matt Riddle, The minimum forcing number for the torus and the hypercube, Discrete Mathematics, 245 (2002) 283-292.
Dan Isaksen and Beth Robinson, Triangle-free polyconvex graphs, Ars Combinatorica, 64 (2002) 259--263.
Joshua Vonkorff, Classification of greedy subset-sum-distinct sequences, Discrete Mathematics, 271 (2003) 271-282.

2000 - Funded by NSF/NSA/UMD

Student Participants: Thomas Carlson, Josh Greene, Manish Patnaik, Sarah Moss, Ben Reichardt, Melanie Wood.
Research advisers: Mike Develin*, Stephen Hartke*.
Visitors: Aaron Archer*, Daniel Biss*, Samit Dasgupta*, Marci Gambrell*, Tricia Hersh, Kiran Kedlaya**,
Davesh Maulik, David Moulton**, Matt Riddle, Lauren Williams*, David Witte**

Thomas Carlson, The edge-isoperimetric problem for discrete tori, Discrete Mathematics, 245 (2002) 33-49.
Mike Develin, Stephen Hartke and David P. Moulton, A general notion of visibility graphs, Journal of Discrete and Computational Geometry , 29 (2003) 511-524.
Manish Patnaik, Isometry dimension of finite groups, Journal of Algebra, 246 (2001) 641-646.
Josh Greene, Chromatic capacities of graphs and hypergraphs, Discrete Mathematics, 281 (2004) 197-207.
Melanie Wood, P-orderings: a metric viewpoint and the non-existence of simultaneous orderings, Journal of Number Theory, 99 (2003) 36-56.

2001 - Funded by NSF/NSA/UMD

Student Participants: Kelli Carlson, Andy Cotton, Geir Helleloid, Elena Grigorescu, Kate Ponto,
Jan Siwanowicz, Phil Matchett, Joe Rabinoff
Research advisers: Mike Develin*, Stephen Hartke*
Visitors: Josh Greene, Dan Isaksen**, Davesh Maulik*, David Moulton**, Manish Patnaik*, Matt Riddle, Steve Wang*, David Witte**, Melanie Wood

Kelli Carlson, Generalized books and C_m snakes are prime graphs, Ars Combinatoria, 80 (2006) 215-221.
Geir Helleloid, Connected triangle-free m-step competition graphs, Discrete Applied Mathematics, 145 (2005) 376-383.
Elena Grigorescu, Decreasing the diameter of cycles, Journal Graph Theory 43 (2003) 299-303.
Elena Grigorescu, The insulation sequence of a graph, Discrete Applied Mathematics, 134 (2004) 77-90.
Stephen Hartke and Kathleen Ponto, k-ordered Hamiltonicity of iterated line graphs, Discrete Mathematics, 309 (2009) 1491-1497.
Phil Matchett, Operations on well-covered graphs and the roller-coaster conjecture, The Electronic Journal of Combinatorics, 11 (2004) R45, 17 pages.
Joe Rabinoff, Hybrid grids and the Homing Robot, Discrete Applied Mathematics, 140 (2004) 155-168.

2002 - Funded by NSF/NSA/UMD

Student Participants: David Arthur, Denis Chebikin, Ellen Eischen, Elena Grigorescu, Wei Ho, Seth Kleinerman,
Peter Lee, Sasha Schwartz
Research advisers: Geir Helleloid*, Phil Matchett*
Visitors: Daniel Biss**, Andy Cotton, Samit Dasgupta*, Mike Develin*, Stephen Hartke*, Tricia Hersh**,
Tara Holm**, Dan Isaksen**, Kiran Kedlaya**, Andy Matchett**, David Moulton**, Manish Patnaik*,
Cammie Smith*, Jan Siwanowicz, Zvezde Stankova**, Melanie Wood

David Arthur, The restricted arc-width of a graph, The Electronic Journal of Combinatorics, 10 (2003) #R41, 18 pages.
Denis Chebikin, Graph powers and k-ordered Hamiltonicity, Discrete Mathematics, 308 (2008) 3220--3229.
Denis Chebikin, On k-edge-ordered graphs, Discrete Mathematics, 281 (2004) 115-128.
Ellen Eischen, Decomposition of almost complete tripartite graphs into isomorphic factors of fixed diameter, Discrete Mathematics, 306 (2006) 745-761.
Wei Ho, The m-step, same-step, and any-step competition graphs, Discrete Applied Mathematics, 152 (2005) 159-175.
Seth Kleinerman, Bounds on forcing numbers of bipartite graphs, Discrete Mathematics, 306 (2006) 66-73.
Alexander Schwartz, The deficiency of a regular graph, Discrete Mathematics, 306 (2006) 1947-1954.

2003 - Funded by NSF/NSA/UMD

Student Participants: Reid Barton, George Brown, Kelli Carlson, Evan Bullock, Margaret Doig, Sasha Korolova,
Ian Le, Anna Maltseva, Max Maydanskiy, Melanie Wood, Brian Wyman
Research advisers: Geir Helleloid*, Phil Matchett*
Visitors: Abbey Alexander, David Arthur, Evelyn Budd, Denis Chebikins*, Mike Develin**, Patrick Headley**,
Dan Isaksen**, Daniel Kane, Kiran Kidlaya**, Andy Matchett**, Joy Morris**, David Witte Morris**, David Moulton**, Jan Siwanowicz

Reid Barton, Packing densities of patterns, The Electronic Journal of Combinatorics, 11(1) R80 2004 (16 pages).
Evan Bullock, Improved bounds on the length of maximal abelian square-free words, The Electronic Journal of Combinatorics, 11 (2004) #R17, 12 pages.
Kelli Carlson and Mike Develin, On the bondage number of planar and directed graphs, Discrete Mathematics, 306 (2006) 820-826.
Daniel Kane, Generalized base representations, Journal of Number Theory, 120 (2006) 92-100.
Aleksandra Korolova, Ramsey numbers of stars versus wheels of similar sizes, Discrete Mathematics, 292 (2005) 107-117.
Ian Le, Wilf classes of pairs of permutations of length 4, The Electronic Journal of Combinatorics, 12 (2005) R25 26 pages.
Maksim Maydanskiy, The incidence coloring conjecture for graphs of maximum degree 3, Discrete Mathematics, 292 (2005) 131-141.
Melanie Wood, Belyi-extending maps and the Galois action on dessins d'enfants, Publications of the Research Institute for Mathematical Sciences, 42 (2006) 721-737.

2004 - Funded by NSF/NSA/UMD

Student Participants: Melody Chan, Mike Dinitz, Matt Elder, Elena Fuchs, Jack Huizenga, Ricky Liu,
Karola Meszaros, Sasha Ovetsky, Gregory Price
Research advisers: Phil Matchett, Lanie Wood
Visitors: Aaron Archer**, David Arthur*, Reid Barton, Evan Bullock, Denis Chebikin*, Mike Develin**,
Josh Greene*, Stephen Hartke**, Geir Helleloid*, Dan Isaksen**, Max Maydanskiy*, Andy Matchett**,
Joy Morris**, David Witte Morris**, David Moulton**, Sasha Schwartz

Melody Chan, The maximum distinguishing number of a group, The Electronic Journal of Combinatorics, 13(1) R70 2006 (8 pages).
Melody Chan, The distinguishing number of the augmented cube and hypercube powers, Discrete Mathematics, 308 (2008) 2330-2336.
Melody Chan, The distinguishing number of the direct product and wreath product action, Journal of Algebraic Combinatorics, 24 (2006) 331-345.
Mike Dinitz, Full rank tilings of finite abelian groups, SIAM Journal of Discrete Mathematics, 20 (2006) 160-170.
Matt Elder, Path bundles on n-cubes, Discrete Mathematics 308 (2008) 3479-3490.
Elena Fuchs, Longest induced cycles in Cayley graphs, The Electronic Journal of Combinatorics, 12(1) R52 (2005) 12 pages.
Geir Helleloid, Madeeha Khalid, Phil Matchett Wood and David Moulton, Graph pegging numbers, Discrete Mathematics, 309 (2009) 1971-1985.
Ricky Liu, Counting subrings in Zⁿ of index k, Journal of Combinatorial Theory, Series A, 114 (2007) 278-299.
Jack Huizenga, Chromatic capacity and graph operations, Discrete Mathematics, 308 (2008) 2134-2148.
Karola Meszaros, On 3-regular 4-ordered graphs, Discrete Mathematics, 308 (2008) 2149-2155.
Karola Meszaros, On low degree k-ordered graphs, Discrete Mathematics, 308 (2008) 2366-2378
Alexandra Ovetsky, On well-coveredness of Cartesian products of graphs, Discrete Mathematics, 309 (2009) 238-246.

2005 - Funded by NSF/NSA/UMD

Student Participants: Ana Caraiani, Jacob Fox, Jack Huizenga, Daniel Kane, Mark Lipson, Alison Miller,
Mariana Raykova, Steven Sivek, Vidya Venkateswaran
Research advisers: David Arthur*, Phil Matchett*
Visitors: Scot Adams**, Aaron Archer**, Reid Barton*, Daniel Biss**, Evan Bullock*, Denis Chebikin*,
Mike Develin**, Josh Greene*, Stephen Hartke**, Wei Ho*, Geir Helleloid*, Dan Isaksen**, Ian Li*
Max Maydanskiy*, Andy Matchett**, David Moulton**, Manish Patnaik*, Lanie Wood*

Ana Caraiani, Generalizations of multiplicative semigroups related to the 3x+1 problem, Advances in Applied Mathematics, 45 (2010) 373-389.
Jacob Fox, A bipartite analogue of Dilworth's theorem, Order, (2006) 197-209.
Jack Huizenga, The minimum size of complete caps in (Z/nZ)², The Electronic Journal of Combinatorics, 13(1) R58 19 pages.
Daniel M. Kane, Asymptotics of McKay numbers for S_n, Journal of Number Theory, 124 (2007) 200-228.
Daniel M. Kane, Lower Bounds on the size of sums-of-squares formulas, Journal of Number Theory, 128 (2008) 639-644.
Mark Lipson, Completion of Wilf-classification of 3-5 pairs using generating trees, The Electronic Journal of Combinatorics, 13 R31 (2006) 19 pages
Alison Miller, Asympototic bounds for permutations containing many different patterns, Journal of Combinatorial Theory Series A, 116 (2009) 92-108.
Mariana Raykova, Permutation reconstruction from minors, The Electronic Journal of Combinatorics, 13(1) R66 (2006) 14 pages.
Stephen Sivek, Some plethysm results related to Foulkes's conjecture, The Electronic Journal of Combinatorics, 13(1) R24 (2006) 9 pages.
Vidya Venkateswaran, A new class of multiset Wilf equivalent pairs, Discrete Mathematics, 307 (2007) 2508-2513.

2006 - Funded by NSF/NSA/UMD

Student Participants: Jared Bass, Ana Caraiani, Atoshi Chowdhury, Angela Hicks, Matthew Ince, Nate Ince, Nathan Kaplan, Alex Levin, Sherry Wu, Yan Zhang
Research advisers: Reid Barton* and Ricky Liu*
Visitors: Scot Adams**, David Arthur*, George Brown*, Evan Bullock*, Melody Chan*, Mike Develin**, Mike Dinitz*,
Josh Greene*, Stephen Hartke**, Geir Helleloid*, Dan Isaksen**, Daniel Kane, Kiran Kedlaya**, Mark Lipson,
Max Maydanskiy*, Alison Miller, David Moulton**, Sasha Ovetsky*, Steven Sevik*, Lanie Wood*, Phil Matchett Wood*

Jared Bass, Improving the Erdos-Ginsburg-Ziv theorem for some non-Abelian groups, Journal of Number Theory, 126 (2007) 217-236.
Nathan Kaplan, Flat cyclotomic polynomials of order three, Journal of Number Theory, 127 (2007) 118-126.
Nathan Kaplan, New bounds for the maximal height of divisors of xⁿ - 1, Journal of Number Theory, 129 (2009) 2673-2688.

2007 - Funded by NSF/NSA/UMD

Student Participants: Joshua Batson, Hannah Breckbill, Alan Deckelbaum, Ariel Levavi, Tiankai Liu, Maria Monks, Aaron Pixton, Ameya Velingker
Research advisers: Reid Barton* and Ricky Liu*
Visitors: Sarah Spence Adams**, Scot Adams**, David Arthur*, Jared Bass*, Manjul Bhargava**,Mike Develin**, Stephen Hartke**,
Geir Helleloid**, Tricia Hersh**, Dan Isaksen**, Nathan Kaplan*, Kiran Kedlaya**, Alex Levin*,
Alison Miller, Dave Morris**, Joy Morris**, David Moulton**, Lenny Ng**, Lanie Matchett Wood*, Phil Matchett Wood*

Joshua Batson, Nathanson heights in finite vector spaces, Journal of Number Theory , 128 (2008) 2616-2633.
Alan Deckelbaum, Minimum product set sizes in nonabelian groups of order pq, Journal of Number Theory , 129 (2009) 1234-1245.
Ariel Levavi, Pegging numbers for various tree graphs, Ars Combinatoria, 110 (2013) 387-408.
Maria Monks, The solution to the partition reconstruction problem, Journal of Combinatorial Theory, Series A, 116 (2009) 76-91.
Maria Monks, Reconstructing permutations from cycle minors, The Electronic Journal of Combinatorics 16 R19 (2009).
Aaron Pixton, Sequences with small subsum sets, Journal of Number Theory, 129 (2009) 806-817.
Aaron Pixton, Alternators in the Cayley-Dickson algebras, Forum Mathematicum, 21 (2009) 853-869.

2008 - Funded by NSF/DoD/NSA/UMD

Student Participants: Jesse Geneson, Sherry Gong, Kelley Harris, John Kim, Brian Lawrence, Maria Monks,
Nathan Pflueger, Charmanine Sia, Yi Sun
Research advisers: Nathan Kaplan* and Ricky Liu*
Visitors: Scot Adams**, David Arthur*, Jared Bass*, Joshua Batson*, Hannah Breckbill, Ana Caraiani*,
Melody Chan*, Stephen Hartke**, Geir Helleloid**, Jack Huizenga*, Maksim Maydanskiy*, Alison Miller*,
Dave Morris**, Joy Morris**, David Moulton**, Aaron Pixton*, Steven Sivik*, Ameya Velingker, Lanie Matchett Wood*,Phil Matchett Wood*

Jesse Geneson, Extremal functions of forbidden double permutation matrices, Journal of Combinatorics, Series A 116 (2009) 1235-1244.
Sherry Gong, On a problem regarding coefficients of cyclotomic polynomials, Journal of Number Theory, 129 (2009) 2924-2932.
Kelley Harris, On the classification of integers n that divide φ(n) + σ(n), Journal of Number Theory, 129 (2009) 2093-2110.
John Kim, The incidence game chromatic number of certain classes of graphs, Discrete Applied Mathematics, 159 (2011) 683-694.
Maria Monks, Number theoretic properties of generating functions related to Dyson's rank for partitions into distinct parts, Proceedings of the American Mathematical Society, 138 (2010) 481-494.
Maria Monks and Ken Ono, Modular forms arising from Q(n) and Dyson's rank Advances in Applied Mathematics , 46 (2011) 457-466.
Nathan Pflueger, Graph reductions, binary rank, and pivots in gene assembly Discrete Applied Mathematics 159 (2011) 2117-2134.
Charmaine Sia, Hurwitz equivalence in tuples of dihedral groups, dicyclic groups, and semidihedral groups, The Electronic Journal of Combinatorics, 16 (2009) R95 17 pages.
Charmaine Sia, The game chromatic number of some families of Cartesian product graphs, AKCE International Journal of Combinatorics, 6 (2009) 315-327.

2009 - Funded by NSF/DoD/NSA/UMD

Student Participants: Hannah Alpert, Yakov Berchenko-Kogan, Lisa Danz, Samuel Elder, Adam Hesterberg, Eric Riedl, Jacob Steinhardt,
Jonathan Wang, Yufei Zhao Research advisers: Nathan Kaplan* and Nathan Pflueger*
Visitors: Scot Adams**, Jared Bass*, Reid Barton, Alan Deckelbaum*, Geir Helleloid**, Jack Huizenga*,
Jesse Geneson, Kelley Harris*, Brian Lawrence, Ricky Liu*, Tiankai Liu*, Marie Monks, Dave Morris**,
Joy Morris**, David Moulton**,Sasha Frandkin Ovetsky*, Aaron Pixton*, Yi Sun, Lanie Matchett Wood**,
Phil Matchett Wood**, Yan Zhang

Hannah Alpert, Differences of multiple Fibonacci numbers, Integers, 9 A57 (2009) 745-749
Hannah Alpert, Finite phase transitions in countable abelian groups, Archiv der Mathematik, 96 (2011) 311-320.
Hannah Alpert, Rank numbers of grid graphs, Discrete Mathematics, 310 (2010) 3324-3333.
Adam Hesterberg, Extremal functions of excluded tensor products of permutation matrices, Discrete Mathematics, 312 (2012) 1646-1649.
Eric Riedl, Largest minimal percolating sets in hypercubes under 2-bootstrap percolation, The Electronic Journal of Combinatorics, 17 (2010) R80 13 pages.
Eric Riedl, Largest and smallest minimal percolating sets in trees, The Electronic Journal of Combinatorics, 19 (2012) P64 18 pages.
Jacob Steinhardt, Permutations with ascending and descending blocks, The Electronic Journal of Combinatorics,17 (2010) R14 28 pages.
Jonathan Wang, A new infinite family of minimally nonideal matrices, Journal of Combinatorial Theory, Series A, 118 (2011) 365-372.
Jonathan Wang, Thin Lehman matrices and their graphs, The Electronic J. of Combinatorics, 17 (2010) R165 24 pages.
Yakov Berchenko-Kogan, Minimal product sets sizes in nonabelian groups, Journal of Number Theory, 132 (2012) 2316-2335.
Yufei Zhao, Constructing MSTD sets using bidirectional ballot sequences, Journal of Number Theory, 130 (2010), 1212-1220.
Yufei Zhao, The number of independent sets in a regular graph, Combinatorics, Probability and Computing, 19 (2010) 315-320.
Yufei Zhao, Counting MSTD sets in finite Abelian groups, Journal of Number Theory, 130 (2010) 2308-2322.
Yufei Zhao, Sets characterized by missing sums and differences, Journal of Number Theory, 11 (2011) 2107-2134.
Yufei Zhao (with David Galvin), The number of independent sets in a graph with small maximum degree, Graphs and Combinatorics, 27 (2011) 177-186.

2010 - Funded by NSF/DoD/NSA/UMD

Student Participants: Eva Belmont, Emily Berger, Tiffany Cai, Adam Hesterberg, Delong Meng, Jeff Manning, Lauren McGough, David Rolnick, Krishanu Sankar, Alex Zhai
Research advisers: Maria Monks* and Nathan Pflueger*
Visitors: Scot Adams**, Cammie Smith Barnes**, Jared Bass*, Mike Develin**, Sam Elder, Nathan Kaplan*,
Yakov Berchenko-Kogan, Ariel Levavi*, Alison Miller*, Evan O'Dornay, Eric Riedl*, Jacob Steinhardt
Jonathan Wang, Geir Helleloid**, Jack Huizenga*, Ricky Liu**, David Moulton**, Aaron Pixton*, Yi Sun*

Eva Belmont, Paths that are m-step competition graphs, Discrete Applied Mathematics, 159 (2011) 1381-1390.
Jeff Manning, EZADS inputs which produce half-factorial block monoids, Semigroup Forum, 90 (2015), no. 3, 775-799.
Delong Meng, Boolean elements in the Bruhat order on twisted involutions, Involve, 5 No. 3 (2012) 339-348.
David Rolnick, The on-line degree Ramsey number of cycles, Discrete Mathematics, 313 (2013) 2084-2093.
David Rolnick, Trees with an on-line degree Ramsey number of four, The Electronic Journal of Combinatorics, 18 (2011) #P173 21 pages.
Krishanu Sankar, Achievable sets in Zⁿ, Forum Mathematicum, 27 (2105) 57-76.
Alex Zhai, Fibonacci-like growth of numerical semigroups of a given genus, Semigroup Forum, (3) 86 (2013) 634-662.
Alex Zhai, An asymptotic result concerning a question of Wilf, (2011) arXiv:1111.2779 [math.CO] 9 pages.

2011 - Funded by NSF/DoD/NSA/UMD

Student Participants: Noah Arbesfeld, John Berman, Carolyn Kim, Gaku Liu, Jeff Manning, Margaret Meyerhofer, David Rolnick, Rik Sengupta, Lynnelle Ye
Research advisers: Alan Deckelbaum* and Jonathan Wang*
Visitors: Scot Adams**, Hannah Alpert, Cammie Smith Barnes**, Jared Bass*, Nathan Kaplan*,
Yakov Berchenko-Kogan, Ricky Liu**, Delong Meng, Alison Miller*, Ricky Liu**, David Moulton**,
Aaron Pixton*, Yi Sun*, Nathan Pflueger, Alex Zhai

Noah Arbesfeld Partial permutations avoiding pairs of patterns, Discrete Mathematics, 313 (2013) 2614-2623.
Gaku Liu, Minimum clique number, chromatic number, and Ramsey numbers, The Electronic Journal of Combinatorics, 19 (2012) #P55 10 pages.
Nathan Kaplan and Lynnelle Ye, The proportion of Weierstrass semigroups, Journal of Algebra, 373 (2013) 377-391.
David Rolnick, On the classification of Stanley sequences, European Journal of Combinatorics , 340 (2017) 51-70 arXiv:1408.1940

2012 - Funded by NSF/DoD/NSA/UMD

Student Participants: Ben Bond, Sachi Hashimoto, Yang Jiao, Ben Kraft, Daniel Kriz, Irene Lo, Evan O'Dorney, Ping Ngai (Brian) Chung, Kate Rudolph, Jonathan Sheperd
Research advisers: Adam Hesterberg, Eric Riedl* and Davie Rolnick
Visitors: Scot Adams**, Hannah Alpert*, Jared Bass*, Yasha Berchen-Kogan*, John Berman, Melody Chan**, Mike Develin**, Sam Elder*,
Nathan Kaplan*, Brian Lawrence*, Carolyn Kim, Gaku Liu*, Alison Miller*, David Moulton**, Aaron Pixton*, Nathan Pflueger*,
Krishau Sankar*, Rik Sengupta*, Charmaine Sia*, Cammie Smith**, Yi Sun*, Jonathan Wang*, Lynnette Ye

Ben Bond, EKR sets for large n and r, Graphs and Combinatorics, 32 (2016) 495-510.
Brian Chung, On the c-strong chromatic number of t-intersecting hypergraphs, Discrete Mathematics, 313 (2013) 1063-1069.
Yang Jiao, On the Sprague-Grundy values of the F-Wythoff game, The Electronic Journal Combinatorics, 20(1) (2013) #P14.
Ben Kraft, Diameters of Cayley graphs generated by transposition trees, Discrete Applied Mathematics,} 184} (2015) 178-188.
Daniel Kriz, On the maximal cross number of unique factorization multisets, Journal of Number Theory, 133 (2013) 3033-3056.
Irene Lo, Misere Hackenbush flowers, srXiv:1212.5937
Irene Lo, Bounds on the rainbow connection number of κ-connected graphs, arXiv:1212.5934
Evan O'Dorney, Degree asymptotics of the numerical semigroup tree, Semigroup Forum, 87 (2013) 601-616.
Kate Rudolph, Pattern popularity in 132-avoiding permutations, The Electronic Journal Combinatorics, 20(1) (2013) #P8.

2013 - Funded by NSF/DoD/NSA/UMD

Student Participants: Levent Alpoge, Lynn Chua, Michael Druggan, Albert Gu, Ben Gunby, Xiaoyu He, Keenan Monks, Soohyun Park, Caitlin Stanton
Research advisers: Sam Elder and Krishanu Sankar
Visitors: Noah Arbesfeld*, Ben Bond*, Tim Chow**, Brian Chung, Yang Jiao, Daniel Kriz, Maria Monks*, Davis Moulton**, Aaron Pixton**, David Rolnick*, Lynnelle Ye

Levent Alpoge, Self-conjugate core partitions and modular forms, Journal of Number Theory, 140 (2014) 60-92.
Levent Alpoge, Proof a conjecture of Stanley-Zanello, Journal of Combinatorial Theory Series A, 125 (2014) 166-176.
Lynn Chua and Krishanu Sankar, Equipopularity classes of 132-avoiding permutations, The Electronic Journal of Combinatorics, 21(1) (2014) #P.1.59 17 pages.
Albert Gu, Sprague-Grundy Values of the R-Wythoff game, The Electronic Journal of Combinatorics 22(2) (2015) #P2.13, 15 pages.
Benjamin Gunby, The maximal length of a k-separator permutation, The Electronic Journal Combinatorics, 21(3) (2014) #P3.19, 14 pages
Benjamin Gunby (with Axel Bacher, Antonio Bernini, Luca Ferrari, Renzo Pinzani, and Julian West), The Dyck pattern poset, Discrete Mathematics, 321 (2014) 12-23.
Xiaoyu He, Cross number invariants of finite abelian groups, Journal of Number Theory, 130 (2014) 100-117.
Caitlin Stanton, Packing polynomials on sectors of R², Integers: Electronic Journal of Combinatorial Number Theory, 14 (2014) #A67, 13 pages.

2014 - Funded by NSF/DoD/NSA/UMD

Student Participants: Amol Aggarwal, Maddie Brandt, Xiaoyu He, Bumsoo Kim, Vivian Kuperberg, Alex Lombardi, Ashvin Swaminathan, Praveen Venkataramana, Samuel Zbarsky
Research advisers: Noah Arbesfeld, Adam Hesterberg, Daniel Kriz
Visitors: Aaron Abrams**, Levent Alpoge*, Tim Chow**, Sam Elder*, Maria Monks Gillespie*, Ben Gunby, Sachi Hashimoto*,
Brian Lawrence*, Irene Lo*, Lew Ludwig**, Ebad Mahmoodian**, David Moulton**, Rishi Nath**, Soohyan Park, Nathan Pflueger**,
Eric Riedl*, Davie Rolnick*, Caitlin Stanton*, Melanie Wood**, Phil Matchett Wood**

Amol Aggarwal, Armstrong's conjecture for (k,mk+1)-core partitions, European Journal of Combinatorics, 47 (2015) 54-67. arXiv:1407.5134
Amol Aggarwal, When does the set of (a,b,c)-core partitions have a unique maximal element? The Electronic Journal of Combinatorics, 22(2) (2015) #P2.31, 10 pages. arXiv: 1408.0550
Madeline Brandt, Quadratic packing polynomials on sectors of R², arXiv:1409.0063
Xiaoyu He, Zero-sum subsequences of length kq over finite Abelian p groups, Discrete Mathematics, , 339 (1) (2016) 399-407.
Xiaoyu He, Geometric progression-free sequences with small gaps, Journal of Number Theory, 151 (2015) 197-210.
Bumsoo Kim, The cross number of zero-sum free sequences in finite Abelian groups, Journal of Number Theory, 157 (2015) 99-122. arxiv.org/pdf/1410.6867.pdf
Vivian Kuperberg, Hadamard matrices modulo p and small modular Hadamard matrices, Journal of Combinatorial Designs, 24 (3) (2016) 393-405. arXiv:1409.0148
Alex Lombardi, Distinguishing extension numbers for Rⁿ and Sⁿ, arXiv:1408.5849
David Rolnick and Praveen S. Venkataramana, On the growth of Stanley sequences, Discrete Mathematics, 338 (2015) 1928-1937. arXiv:1408.4710
Ashvin Swaminathan, On arboreal Galois representations of rational functions, Journal of Algebra, 448 (2016) 104-126. arXiv:1407.7012
Samuel Zbarsky, Unimodality of partitions in near-rectangular Ferrers diagrams, Discrete Mathematics, 338 (2015) 1649-1658. arXiv:1408.3895.
Samuel Zbarsky, The maximum number of subset divisors of a given size, Discrete Mathematics , 339(6) 2016) 1727-1733. arXiv:1407.4720

2015 - Funded by NSF/NSA/UMD

Student Participants: Matthew Brennan, Calvin Deng, Bill Kuszmaul, Mitchell Lee, Bobby Shen, Jonathan Tidor, Ashvin Swaminathan, Sahana Vasudevan, Victor Wang, Maddie Weinstein, Chen Xie
Research advisers: Levent Alpoge, Ben Gunby
Visitors: Amol Aggarwal*, Hannah Alpert*, Noah Arbesfeld*, Tim Chow**, Albert Gu*, Xiaoyu He, Adam Hesterberg*, Samuel Judge*, Alex Lombardi,
Alison Miller**, David Moulton**, Rishi Nath**, Aaron Pixton**, Krishanu Sankar*, Robert Stingley**, Ian Whitehead**, Melanie Matchett Wood**, Phil Matchett Wood**, Lynnelle Ye*

Matthew Brennan, Ramsey numbers of trees and unicylic graphs versus fans, Discrete Mathematics, 340 (2017) 969-983. arXiv:1511.07306
Matthew Brennan, Ramsey numbers of trees versus odd cycles, The 'Electronic Journal of Combinatorics, 23(3) (2016) #P3.2, 12 pages, arXiv:1511.07541
Calvin Deng, Even (bar s,bar t)-core partitions and self-associate characters of ∼S_n, Discrete Mathematics, 342 (2019) 540-545. . arXiv:1508.01462
Calvin Deng, Davenport constant for commutative rings, Journal of Number Theory, 172 (2017) 321-342. arxiv.org/abs/1602.03445
Noam D. Elkies and Ashvin Swaminathan, Permutations that destroy arithmetic progressions in elementary p-groups, The Electronic Journal of Combinatorics, 24(1) (2017) #P1.20, 12 pages.
William Kuszmaul, Signed enumeration of upper-right corners in path shuffles, European Journal of Combinatorics , 60 (2017) 100-113, arXiv:1510.00777
William Kuszmaul, Fast algorithms for finding pattern avoiders and counting pattern occurrences in permutations, Mathematics of Computation, 987-1011. arXiv:1509.08216
Mitchell Lee, Sets with few differences in abelian groups, The Electronic Journal of Combinatorics, 25(3) (2018) #P3.19, 12 pages.
Bobby Shen, Parametrizing an integer linear program by an integer, SIAM Journal of Discrete Mathematics, 32(1) (2018) 173-190. arXiv:1510.01343
Bobby Shen, The parametric Frobenius problem and parametric exclusion, arXiv:1510.01349
Jonathan Tidor, Dense binary PG(t-1,2)-free matroids have critical number t-1 or t, Journal of Combinatorial Theory Series B, 124 (2017) 165-179 arXiv:1508.07278
Victor Wang, Simultaneous core partitions: parameterizations and sums, The Electronic J. Combinatorics. 23(1) (2016), #P1.4, 34 pages.
Victor Wang, On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields, Journal of Number Theory, 160, (2016) 492-515. arXiv:1508.06552
Madelina Weinstein, Invariance of the Sprague-Grundy function for variants of Wythoff's game, Integers: Electronic Journal of Combinatorial Number Theory, 16 (2016) \# G4, 13 pages. arXiv:1507.04665

2016 - Funded by NSF/NSA/UMD

Student Participants: Ryan Alweiss, Aaron Berger, Evan Chen, Pad Jiradilok, Sammy Luo, Colin Defant, Shyam Narayanan, Yelena Mandelshtam, Nina Zubrilina
Research advisers: Levent Alpoge, Ben Gunby
Visitors: Matt Brennan, Sam Elder, Maria Monks Gillespie**, Bryan Gillespie*, Samuel Judge*, Nathan Kaplan**, Aaron Landesman*, Mitchell Lee*, Alex Lombardi*, David Moulton**, Rishi Nath**, Aaron Pixton**, Eric Reidl*, Jonathan Tidor, Victor Wang, Maddie Weinstein*, Phil Matchett Wood**, Melanie Matchett Wood**

Ryan Alweiss, Asymptotic results on Klazar set partition avoidance, Discrete Mathematics and Theoretical Computer Science, 19(2) (2018) 8 pp. arXiv:1608.02279
Ryan Alweiss, Ramsey numbers of odd cycles versus larger even wheels, Discrete Mathematics, 341 (2017) 981-989. arXiv:1609.03672
Aaron Berger, An analogue of Erdos-Ginzburg-Ziv Theorem over Z, Discrete Mathematics, 34(4) 342(3) (2019) 815-820. arXiv:1608.04125
Aaron Berger, Progressions and paths in colorings of Z, arXiv:1706.01579
Evan Chen, Avoiding algebraic integers of bounded house in orbits of rational functions over cyclotomic closures, Proceedings of the American Mathematical Society, 2018, 144, 4599-4608, arXiv:1608.04146
Evan Chen and Shyam Narayanan, The 26 Wilf-equivalence classes of length five quasi-consecutive patterns, Discrete Mathematics & Theoretical Computer Science, October 24, 2018, vol. 20 no. 2 arXiv:1609.04626
Colin Defant, Some poset pattern-avoidance problems posed by Yakoubov, Journal of Combinatorics 9 (2018), 233-257.arXiv:1608.0395
Colin Defant, Anti-power prefixes of the Thue-Morse word, The Electronic Journal of Combinatorics, 24(1) (2017) #1.32, 17 pages, arXiv:1607.05825
Pakawut Jiradilok, Reconstructing partitions from their multisets of k-minors, arXiv:1610.05354v1
Sammy Luo, Short zero-sum sequences over abelian p-groups of large exponent, Journal of Number Theory, 177 (2017) 28-36. arXiv:1608.05157
Sammy Luo, A counting lemma for binary matroids and applications to extremal problems, Journal of Combinatorial Theory, Series B, 136 (2019) 329-359 arXiv:1610.09587
Yelena Mandelshtam, On graphs representable by pattern-avoiding words, Discussiones Mathematicae Graph Theory, 39 (2019) 375-389. doi:10.7151/dmgt.2128, arXiv:1608.07614 [math.CO]
Shyam Narayanan, Resolving two conjectures on staircase encodings and boundary grids of 132- and 123-avoiding permutations, The Electronic Journal of Combinatorics, 26(3) (2019) P3.62 16pp. arXiv: 1802.06345, 13 pages
Shyam Narayanan, Functions on antipower prefix lengths of the Thue-Morse word, Discrete Mathematcs, 343(2) 2020 111675. arXiv:1705.06310, 15 pages
Nina Zubrilina, On edge dimension of a graph, Discrete Mathematics, 341(7) (2018) 2083-2088. arXiv:1611.01904v1
Nina Zubrilina, Asymptotic behavior of the edge metric dimension of the random graph, Discuss. Math. Graph Theory, 41(2), 589-599. arXiv:1612.06936v1
Nina Zubrilina, Left-right pairs and complex forests of infinite rooted binary trees," International Journal of Number Theory, 16(7) 1637-1642, arXiv:1810.04349

2017 - Funded by NSF/UMD

Student Participants: Evan Chen, Lazar Ilic, Sumun Iyer, Michael Kural, Andrew Kwon, Matt Larson, Mehtaab Sawhney, David Stoner, Nina Zubrilina
Research advisers: Levent Alpoge, Colin Defant, Ben Gunby
Visitors: Hannah Alpert**,Noah Arbesfeld*, Aaron Berger, Tim Chow**, Calvin Deng*, Samuel Judge*, Mitchell Lee*, David Moulton**, Evan O'Dorney*, Davie Rolnick*, Ashvin Swaminathan*, Vidya Venkateswaran**, Melanie Matchett Wood**, Phil Matchett Wood**

Evan Chen, Schur-concavity for avoidance of increasing subsequences in block-ascending permutations, The Electronic Journal of Combinatorics, 24(4) (2017) #4.4, 12 pages arXiv:1708.01350
Evan Chen, A family of partially ordered sets with small balance constant, The Electronic Journal of Combinatorics, 25(4) (2018) #P4.43 13 pages. arXiv:1709.05753
Evan Chen, Multiplicative and exponential variations of orthomorphisms of cyclic groups, Journal of Combinatorics, 11(2) (2020), 377-389. arXiv:1710.02734
Evan Chen, Linear polychromatic colorings of hypercube faces, The Electronic Journal of Combinatorics, 25(1) (2018) #P1.2, 11 pages. arXiv:1609.01247
Colin Defant and Sumun Iyer, Domination and upper domination of direct product graphs, Discrete Mathematics, 341 (2018) 2742-2752. arXiv:1708.01305
Sumun Iyer, Star coloring splitting graphs of cycles, arXiv:1710.03910
Michael Kural, Dedekind sums with even denominators, Journal of Number Theory, 197 (2019) 106-120. arXiv:1801.00517
Michael Kural, Fuss-Schroder paths and rooted plane forests, The Electronic Journal of Combinatorics,, 24(2) (2017) arXiv:1805.05317
Andrew Kwon, A note on minimal additive complements, Discrete Mathematics, 342(7) (2019) 1912-1918. arXiv:1708.01287
Matt Larson, Power maps in finite groups, Integers: Electronic Journal of Combinatorial Number Theory , 19 (2019). #A58, 15pp. arXiv:1707.06696
Richard Moy, Mehtaab Sawhney, and David Stoner, Characters of independent Stanley sequences, European Journal of Combinatorics, 70 (2018) 354-363. arXiv:1708.01849
Mehtaab Sawhney and David Stoner, On a conjecture regarding permutations which destroy arithmetic progressions, The Electronic Journal of Combinatorics, 25(2) (2018) #P2.42, 18 pages arXiv:1708.00144
Mehtaab Sawhney and David Stoner, On symmetric but not cyclotomic numerical semigroups, SIAM Journal of Discrete Mathematics, 32(2) (2018) 1296-1304. arXiv:1707.00782
Mehtaab Sawhney and David Stoner, Hypercube packings and coverings with higher dimensional rooks, Australasian Journal of Combinatorics, 77(1) (2020) 9-34, arXiv:1801.10607 16 pages
Mehtaab Sawhney and Jonathan Tidor, Two classes of modular p-Stanley sequences, Journal of Combinatorics, 11(1) (2020) 127-140. arXiv:1506.07941
Nina Zubrilina, On the generalized sigma divisor function, arXiv:1711.02871

2018 - Funded by NSF/NSA

Student Participants: Niven Achenjang, Amanda Burcroff, Marisa Gaetz, Brice Huang, Caleb Ji, Noah Kravitz, Erik Metz, Ashwin Sah, Danielle Wang
Research advisers: Levent Alpoge, Aaron Berger, Colin Defant
Visitors: Hannah Alpert**, Ryan Alweiss*, Evan Chen*, Tim Chow**, Ben Gunby*, Samuel Judge**, Kiran Kedlaya**, Andrew Kwon, Matt Larson, Brian Lawrence**, Mitchell Lee*, Sammy Luo*, David Moulton**, Jason Schuchardt, David Stoner, Ashvin Swaminathan*, Melanie Matchett Wood**, Phil Matchett Wood**, Shah Roshan Zamir*, Nina Zubrilna

Niven Achenjang and Aaron Berger, On gaps in the closures of images of divisor functions, International Journal of Number Theory, 15(5) (2019) 1023-1036. arXiv:1808.07550 10 pages
Aaron Berger, Caleb Ji, and Erik Metz, On the distribution of range for tree-indexed random walks, European Journal of Combinatorics, 81 (2019) 256-264. arXiv:1808.04261 6 pages
Aaron Berger and Danielle Wang, Modfified Erdos-Ginsberg-Ziv constants for Z/nZ and (Z/nZ)², Discrete Mathematics, 342(4) (2019) 1113-1116. arXiv:1808.08486 5 pages
Amanda Burcroff, (k,λ)-Anti-powers and other patterns in words, The Electronic Journal of Combinatorics, 25(4) 17 pages. arXiv:1807.07945
Amanda Burcroff, Domination parameters of the unitary Cayley graph of Z/nZ, Discussiones Mathematicae Graph Theory, 43 (2023) 95-114. arXiv:1809.04769 17 pages
Coiln Defant and Noah Kravitz, Stack-sorting for words, Australasian Journal of Combinatorics, 77(1) (2020) 51-68. arXiv:1808.09158
Marisa Gaetz, Anti-power j-fixes of the Thue-Morse word, Discrete Mathematics & Theoretical Computer Science, 23(1) (2021) 1-21. arXiv:1808.01528 25 pages,
Caleb Ji, Distinguishing numbers and generalizations, arXiv:1808.01074 18 pages
Noah Kravitz, Harborth constants for certain classes of metacyclic groups, Discrete Mathematics, 342 (2019) 1492-1509. arXiv:1807.04785 25 pages
Noah Kravitz, On the number of simultaneous core partitions with d-distinct parts, Discrete Mathematics, 342 (12) (2019) 1-14. arXiv:1807.08875 19 pages
Noah Kravitz and Ashwin Sah, A stronger connection between the Erdos-Burgess and the Davenport constants, Journal of Number Theory, 210 (2020) 373-388. arXiv:1808.06031 15 pages
Brice Huang, Cyclic descents for general skew tableaux, Journal of Combinatorial Theory Series A, 169 (2020) 1-45. arXiv:1808.04918
Brice Huang, An upper bound on the number of (132,213)-avoiding cyclic permutations, Discrete Mathematics, 342(6) (2019) 1762-1771, arXiv:1808.08462 15 pages
Mitchell Lee and Ashwin Sah, Constraining strong c-Wilf equivalence using cluster poset asymptotics, Advances in Applied Mathematics, 103 (2019) 43-57. arXiv:1807.04921, 11 pages
Erik Metz, Upper and lower bounds on zero-sum generalized Schur numbers, arXiv:1808.03851 19 pages
Ashwin Sah, Improving the 1/3-2/3 conjecture for width two posets, Combinatorica, 41(1) (2020) 99-126. arXiv:1811.01500 20 pages
Danielle Wang, On roots of Wiener polynomials of trees, Discrete Mathematics, 343(1) (2020) 11164 1-9. arXiv:1807.10967 12 pages
Danielle Wang, The Eulerian distribution on involutions is indeed gamma-positive, Journal of Combinatorial Theory Series A, 165 (2019) 139-151. arXiv:1808.0848v1. 10 pages

2019 - Funded by NSF/NSA

Student Participants: Swapnil Garg, Trajan Hammonds, Catherine Lee, Hanna Mularczyk, Alan Peng, Maya Sankar, Alec Sun, Harish Vemuri, Rachel Zhang
Research advisers: Aaron Berger, Colin Defant
Visitors: Niven Achenjang, Ryan Alweiss*, Amanda Burcroff*, Marisa Gaetz, Brice Huang*, Caleb Ji, Noah Kravitz, Michael Kural, Matt Larson*, Brian Lawrence**, Yelena Mandelshtam*, David Moulton**, Shyam Narayanan*, Rishi Nath**, Ashwin Sah, David Stoner*, Shah Roshan Zamir*, Nina Zubrilna*

Amanda Burcroff and Colin Defant, Pattern-avoiding permutation powers, Discrete Mathematics , 343(11) 2020, 112017, arXiv:1907.09451, 14 pages
Colin Defant, Noah Kravitz, and Ashwin Sah, Supertrees, The Electronic Journal of Combinatorics, 27(2) 2020, 1-26, P.2.7, arXiv:1908.03197
Marisa Gaetz and Caleb Ji, Enumeration and extensions of word-representants, Discrete Applied Mathematics (2020) 284 423-433, arXiv:1909:00019 14 pages
Swapnil Garg, Antipowers in uniform morphic words and the Fibonacci word, Discrete Mathematics and Theoretical Computer Science, 23(3) (2021) No. 14, arXiv:1907.10816, 9 pages
Swapnil Garg, New results on Nyldon words derived using an algorithm from Hall set theory, Advances in Applied Mathematics,, 131 (2021) 102249 arXiv:1908.04056, 22 pages
Swapnil Garg and Alan Peng, Classical and consecutive pattern avoidance in rooted forests, Journal of Combinatorial Theory Series A, 194 (2023), 105699, 52 pages. arXiv:2005.08889, 39 pages
Trajan Hammonds, Modified Erdos-Ginzberg-Ziv constants for (Z/nZ)², arXiv:1907.11236, 11 pages
Catherine Lee, Minimum coprime graph labelings, Journal of Integer Sequences, , Article 20.11.4 Vol. 23 (2020) 15 pages.
Hanna Mularczyk, Lattice paths and pattern-avoiding uniquely sorted permutations, Discrete Mathematics and Theoretical Computer Science, 22:2, 2021, #6 arXiv:1908.04025v2, 18 pages
Shyam Narayanan and Alec Sun, Bounds on expected propagation probabilistic zero forcing, European Journal of Combinatorics, 98 (2021) 103405, arXiv: 1909.04482, 20 pages
Maya Sankar, Pattern-avoiding valid hook configurations, Advances in Applied Mathematics, 125 (2021) 102152, 1-28. arxiv.org/abs/1910.08895, 21 pages.
Alec Sun, Zero-sum subsequences in bounded-sum {-r,s}-sequences, Journal of Combinatorial Theory, Series A , 179, April 2021, 105385 arXiv:1907.06623, 26 pages,
Harish Vemuri, Domination in direct products of complete graphs, Discrete Applied Mathematics, 285 (2020) 473-482. {arXiv:1908.02445, 15 pages
Rachel Zhang, C-(k,l)-sum free sets, Journal of Combinatorics and Number Theory, 12(1) (2020) arXiv:2001.00327, 9 pages
Rachel Zhang, The relationship between the composability and splittability of permutation classes, Discrete Mathematics , (2021) 344(4), p.112271 arXiv:1908.02731, 6 page

2020 - Funded by NSF/NSA

Student Participants: Ilani Axelrod-Freed, Katalin Berlow, Michael Ren, Mihir Singhal, Natasha Ter-Saakov, Emily Zhang, Kai Zheng, Fan Zhou, Daniel Zhu
Research Advisors: Amanda Burcroff, Colin Defant, Yelena Mandelshtam
Visitors: Niven Achenjang, Noga Alon, Ryan Alweiss, Aaron Berger, Evan Chen, Tim Chow, Marisa Gaetz, Swapnil Garg, Jesse Geneson, Trajan Hammonds, Xiaoyu He, Brice Huang, Sumun Iyer, Caleb Ji, Noah Kravitz, Andrew Kwon, Matt Larson, Catherine Lee, Sammy Luo, David Moulton, Shyam Narayanan, Alan Peng, Ashwin Sah, Maya Sankar, Mehtaab Sawhney, David Stoner, Alec Sun, Harish Vemuri, Nina Zubrilina.

Ilani Axelrod-Freed, 312-avoiding reduced valid hook configurations and duck words, Journal of Enumerative Combinatorics and Applications, ECA 1:2 (2021) Article #S2R14 13 pages arXiv:2010.11834
Katalin Berlow, Restricted stacks as functions, Discrete Mathematics, 344(11) (2021) arXiv:2008.01164, 14 pages.
Colin Defant and Kai Zheng, Stack-sorting with consecutive-pattern-avoiding stacks, Advances in Applied Mathematics, 128 (2021) 102192, 33 pages. arXiv 2008.12297
Mihir Singhal, Unimodality of a renement of Lassalle's sequence, Discrete Math. , 346 (2023) arXiv:2008.08222, 8 pages
Mihir Singhal, Families with no perfect matchings, Combinatorial Theory, 1 no. 2 (2021) 1-25. https://escholarship.org/uc/item/1vc250fj
Michael Ren, Wilf equivalences and Stanley-Wilf limits for patterns in rooted labeled forests, European Journal of Combinatorics, to appear. arXiv:2007.12690, 35 pages.
Michael Ren, Wilf equivalences for patterns in rooted labeled forests, Advances in Applied Mathematics, to appear, arXiv:2310.02499, 16 pages.
Michael Ren and Shyam Narayanan, Circular trace reconstruction, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), (185) pp. 18:1-18:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.ITCS.2021.18. arXiv:2009.01346, 22 pages
Natalya Ter-Saakov and Emily Zhang, Extremal pattern-avoiding words, arXiv:2009.0186 10 pages
Emily Zhang, On the broadcast dimension of a graph, Australasian Journal of Combinatorics, 85(3) (2023) 313–339. arXiv:2008.01056, 23 pages.
Kai Zheng, On the e-positivity of trees and spiders,  Journal of Combinatorial Theory . Ser. A., 2022, 105608 , arXiv:2008.05038, 22 pages.
Fan Zhou, On eventually periodic sets as minimal additive complements, The Electronic Journal of Combinatorics, 30(4) (2023), #P4.34 40 pages. arXiv:2010.12162, 32 pages
Daniel G. Zhu, Coloring bipartite graphs with semi-small list size, Annals of Combinatorics, January (2023) 23 pages. https://doi.org/10.1007/s00026-022-00633-z arXiv:2008.06040 [math.CO] 16 pages.
Daniel G. Zhu, Sub-Fibonacci behavior in numerical semigroup enumeration, Combinatorial Theory, 3(2) (2023), #10. doi: 10.5070/C63261988 arXiv:2202.05755 [math.CO] 18 pages.

2021 - Funded by NSF/NSA

Student Participants: Kiril Bangachev, Caleb Fong, Milan Haiman, Carina Letong Hong, Ryan Jeong, Rupert Li, James Lin, Rachana Madhukara, Grace O'Brien, Benjamin Przybocki
Research Advisors: Amanda Burcroff, Colin Defant, Yelena Mandelshtam, Noah Kravitz
Visitors: Aaron Berger, Katalin Berlow, Evan Chen*, Swapnil Garg, Ben Gunby*, Andrew Kwon*, Brian Lawrence**, Mitchell Lee, David Moulton**, Shyam Narayanan*, Michael Ren, Alan Peng, Maya Sankar*, Mehtaab Sawhney**, Alec Sun*, Emily Zhang, Kai Zheng, Fan Zhou, Daniel Zhu, Nina Zubrilina*.

Kiril Bangachev, On the asymmetric generalizations of two extremal questions on friends-and-strangers graphs, European Journal of Combinatorics, 104 (2022) 26 pages, arXiv:2107.06789, 28 pages
Amanda Burcroff and Grace O'Brien, Unimodality and montonic portions of certain domination polynomials, arxiv2110.00709, 17 pages
Colin Defant and James Lin, Rowmotion on m-Tamari and bicambrian lattices, arXiv:2208.10464, 34 pages Combinatorial Theory ,104 (2022) 46 pages, \url{https://escholarship.org/uc/item/5x945586}
Milan Haiman, The dimension of divisibility orders and multiset posets, Order , to appear. arXiv:2201.12952, 16 pages
Letong Hong, The Pop-stack-sorting operator on Tamai lattices, Advances in Applied Mathematics, 139 (2022) 102362, 13 pages. https://arxiv.org/pdf/2201.10030.pdf
Letong Hong and Rupert Li, Length-four pattern avoidance in inversion sequences, Electronic Journal of Combinatorics,} \ 29(4) 2022 arxiv.org/abs/2112.15081 15 pages.
Ryan Jeong, Diameters of friends-and-strangers graphs, Combinatorial Theor y, (4) (2) (2024) #2. Ryan Jeong, On structural aspects of friends-and-strangers graphs, arXiv:2203.10337 [math.CO], 32 pages.
Rupert Li, The spum and sum-diameter of graphs: labelings of sum graphs, Discrete Mathematics, 345(5) (2022), 112806. arXiv:2107.09025, 38 pages.
Rupert Li, Vincular pattern avoidance on cyclic permutations, Enumerative Combinatorics and Applications, 2:4 (2022) Article #S4PP3, 20 pages. https://doi.org/10.54550/ECA2022V2S4PP3, arXiv:2107.12353, 31 pages.
Rachana Madhukara, Adjacency and broadcast dimension of grid and directed graphs, arXiv:2208.11001, 16 pages.
Benjamin Przybocki, Lengths of irreducible and delicate words, Electronic Journal of Combinatorics, 29(3):Paper No. 3.7 (2022) arXiv:2108.06646, 12 pages.

2022 - Funded by Jane Street Capital/NSA

Student Participants: Ankit Bisain, Yunseo Choi, Eliot Hodges, Anqi Li, Sean Li, Jonas Iskander, Katherine Tung, Nathan Sun, Andrei Mandelshtam, Aleksa Milojectvic
Research Advisors: Amanda Burcroff, Colin Defant, Noah Kravitz
Visitors: Niven Achenjang*, Kiril Bangachev*, Katalin Berlow, Swapnil Garg, Edi Gnang**, Carina Letong Hong*, Andrew Kwon*, Brian Lawrence**, Mitchell Lee, Rupert Li, James Lin, Rachana Madhukara, Yelena Mandelshtam*, David Moulton**, Michael Ren, Maya Sankar*, Alec Sun*, Emily Zhang*

Ankit Bisain, Generic classification and asymptotic enumeration of dope matrices, Bulletin of the London Mathematical Society, accepted. arXiv:2209.13811 18 pages.
Yunseo Choi, Counting crucial permutations with respect to monotone patterns, Discrete Mathematics, to appear. arXiv:2208.13469, 21 pages.
Yunseo Choi and Nathan Sun, The image of the pop operator on various lattices, Advances in Applied Mathematics 154 (2024) 102649. arXiv:2209.13695, 23 pages
Yuji Choi and Yunseo Choi, Highly sorted permutations with respect to a 312-avoiding stack, Enumerative Combinatorics and Applications, 3:1 (2023) Article #S2R7 https://doi.org/10.54550/ECA2023V3S1R7
Colin Defant, Rupert Li, James Propp, Benjamin Young, Tilings of benzels via the Stanton--White bijection, Combinatorial Theory 3 (2023). arxiv.org/pdf/2209.05717, 20 pages.
Eliot Hodges, On promotion and quasi-tangled labelings of posets, Annals of Combinatorics, , 28 (2024) 529–554. arXiv:2208.08665, 21 pages.
Rupert Li, Dual linear programming bounds for sphere packing via discrete reductions, arXiv:2206.09876, 20 pages.
Sean Li, Counting numerical semigroups by Frobenius number, multiplicity and depth, Combinatorial Theory , 3 (3) (2023), #6, 1-29. arXiv:2208.1458, 20 pages.
Sean Li, On the number of generalized numerical semigroups, arXiv:2212.13740, 21 pages. Electronic Journal of Combinatorics, to appear.
Andrei Mandelshtam, On fractal patterns in Ulam words,arXiv:2211.14229, 44 pages.
Aleksa Milojevic, Connectivity of old and new models of friends-and-strangers graphs, arXiv:2210.03864, 30 pages.
Nathan Sun, On d-permutations and pattern avoidance classes, arXiv:2209.06087v1, Annals of Combinatorics, 17 (2022). 14 pages.
Nathan Sun, A complete enumeration of ballot permutations avoiding sets of small patterns, Enumerative Combinatorics and Applications, 3:1 (2023) Article #S2R6 https://doi.org/10.54550/ECA2023V3S1R6---arXiv:2208.08506, 18 pages.
Katherine Tung, A bijection between evil-avoiding and rectangular permutations, Electronic Journal of Combinatorics, 30(4) (2023), #P4.8 arXiv:2301.09530, 19 pages.

2023 - Funded by Jane Street Capital/NSA

Directors: Joe Gallian and Colin Defant
Student Participants: Kevin Cong, Sanjana Das, Zach Halberstam, Eliot Hodges, Ilaria Seidel, Eric Shen, Tomasz Slusarczyk, Yaxin (Casey) Qi, Janabel Xia, Honglin Zhu
Research Advisors: Noah Kravitz, Yelena Mandelshtam, Maya Sankar
Visitors: Ankit Bisain, Katalin Berlow, Evan Chen, Ryan Jeong, Andrew Kwon, Mitchell Lee, Andrei Mandelshtam, Rachana Madhukara, Hanna Mularczyk, David Moulton, Carl Schildkraut, Alex Sun, Nathan Sun, Katherine Tung, Daniel Zhu

PJ Appruzzese and Kevin Cong, On two orderings of lattice paths, arXiv:2310.16963, 11 pages.
Grant Barkley, Colin Defant, Eliot Hodges, Noah Kravitz, and Mitchell Lee, Bender-Knuth billards in Coxeter groups, arxiv:2401.17360.pdf, 51 pages.
Kevin Cong, On integer sets excluding permutation pattern waves, arXiv:2308.15695, 14 pages.
Sanjana Das, Bounds for the local properties problem for difference sets, arXiv:2310.13999, 32 pages.
Eliot Hodges, The distribution of sandpile groups of random graphs with their pairings, Trans. Amer. Math. Soc. 377 (2024), 8769-8815 DOI: https://doi.org/10.1090/tran/9244, 48 pages
Yaxin (Casey) Qi, Graph reconstruction from connected triples, arXiv:2309.10113, 21 pages.
Ilaria Seidel and Nathan Sun, Periodic points of consecutive-pattern-avoiding stack-sorting maps, arxiv.org/abs/2308.05868} 8 pages.
Eric Shen, Tighter bounds on the expected absorbing time of Ungarian Markov chains, arXiv:2405.11728, 26 pages.
Janabel Xia, Deterministic stack-sorting for set partitions, arXiv:2309.14644, 11 pages.
Honglin Zhu, The maximum number of cycles in a triangular-grid billiards system with a given perimeter, arxiv:2309.00100, 20 pages.
Honglin Zhu, Evacuating "O"- and "Y"-shaped houses on fire: the connectivity of friends-and-strangers graphs on complete multipartite graphs, arXiv:2307.08121, 23 pages.

2024 - Funded by Jane Street Capital/NSF/Ray Sidney/Eric Wepsic

Directors: Joe Gallian and Colin Defant
Student Participants: Charles Gong, Tuong Le, Derek Liu, Annabel Ma, Nathan Sheffield, Zoe Xi, Lucy Xiao, Edwin Xie, Sophie Zhu
Research Advisors: Noah Kravitz, Mitchel Lee, Maya Sankar
Visitors: Levent Alpoge, Grant Barkley, Katalin Berlow, Evan Chen, Eliot Hodges, Jonas Iskander, Andrew Kwon, Yelena Mandelshtam, David Moulton, Ben Przybocki, Carl Schildkraut, Ilaria Seidel, Alex Sun, Janabel Xia

Charles Gong, Minimizing monochromatic subgraphs of K_{n,n}, arXiv:2410.19076, 35 pages.
Charles Gong, Slitherlink on triangular grids, arXiv:2410.19078, 18 pages.
Annabel Ma, On the bivariate characteristic polynomial of the shuffle lattice, arXiv:2409.17123, 21 pages.
Zoe Xi, Variants of Baranyai's theorem with additional conditions, arXiv:2410.08513, 15 pages.
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Bibliography of the Duluth Summer Research Programs 1977 - 2024