\

Bibliography of the Duluth Summer Research Programs
1977 - 2014

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, 11 (1987) 21-24.

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 Zn[i] into Zm[i] and Zn[r] into Zm[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 An, 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 Zn to Zm, 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 D4k, 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 unn(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 Zd and permutations with no long increasing subsequences, 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, 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
Visitors: Aaron Archer*, Daniel Biss* (research adviser), Samit Dasgupta (research adviser), 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 Wn, Ars Combinatoria, 63 (2002) 273-287.
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 Cm 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, J. 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, 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, 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, Lanie 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, Electronic Journal of Combinatorics, 11(1) R80 2004 (16 pages).
Evan Bullock, Improved bounds on the length of maximal abelian square-free words, 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, 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 Instititute 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, 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, 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, Electronic Journal of Combinatorics, 13(1) R58 19 pages.
Daniel M. Kane, Asymptotics of McKay numbers for Sn, 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, 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, Electronic Journal of Combinatorics, 13(1) R66 (2006) 14 pages.
Stephen Sivek, Some plethysm results related to Foulkes's conjecture, 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, 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, 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, Electronic Journal of Combinatorial Theory, 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, Electronic Journal of Combinatorics, 17 (2010) R80 13 pages.
Eric Riedl, Largest and smallest minimal percolating sets in trees, Electronic Journal of Combinatorics, 19 (2012) P64 18 pages.
Jacob Steinhardt, Permutations with ascending and descending blocks, Electronic Journal of Combinatorics,17 (2010) R14 28 pages.
Jonathan Wang, A new infinite family of minimally nonideal matrices, Journal of Combinatorics, 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, to appear.
Delong Meng, Boolean elements in the Bruhat order on twisted involutions, Involve, 5 No. 3 (2012) 339-348.
Delong Meng, Reduced decompositions and commutation classes, Contributions to Discrete Mathematics, to appear.
David Rolnick, The on-line degree Ramsey number of cycles, Discrete Mathematics, 313 (2013) 2084-2093. http://www.sciencedirect.com/science/article/pii/S0012365X13001933
David Rolnick, Trees with an on-line degree Ramsey number of four, Electronic Journal of Combinatorics, 18 (2011) #P173 21 pages.
Krishanu Sankar, Achievable sets in Zn, Forum Mathematicum, to appear.
Alex Zhai, Fibonacci-like growth of numerical semigroups of a given genus, Semigroup Forum, (3) 86 (2013) 634-662.

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.
John Berman, Cyclic closures of finitely simple pattern classes, submitted.
David Rolnick, On the classification of Stanley sequences.
Gaku Liu, Minimum clique number, chromatic number, and Ramsey numbers, 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.

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, to appear.
Brian Chung, On the c-strong chromatic number of t-intersecting hypergraphs, Discrete Mathematics, 313 (2013) 1063-1069.
Sachi Hashimoto, Sharper lower bounds in the maximum degree and diameter bounded subgraph problem in the mesh, submitted.
Yang Jiao, On the Sprague-Grundy values of the F-Wythoff game, Electronic Journal Combinatorics, 20(1) (2013) #P14.
Daniel Kriz, On the maximal cross number of unique factorization multisets, Journal of Number Theory, 133 (2013) 3033-3056.
Irene Lo, Misere Hackenbush flowers, submitted.
Evan O'Dorney, Degree asymptotics of the numerical semigroup tree, Semigroup Forum, 87 (2013) 601-616.
Kate Rudolph, Pattern popularity in 132-avoiding permutations, 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, Electronic Journal of Combinatorics, 21 (1) (2014) #P.1.59 17 pages
Xiaoyu He, Cross number invariants of finite abelian groups, Journal of Number Theory, 130 (2014) 100-117.
Benjamin Gunby, The maximal length of a k-separator permutation, submitted to 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.
Soohyun Park, Arithmetic properties of generalized Fibonacci sequences, Integers: Electronic Journal of Combinatorial Number Theory submitted.
Caitlin Stanton, Packing polynomials on sectors of R2, Electronic Journal of Combinatorial Number Theory, to appear.

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**


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