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.

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.

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.

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.

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.

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.

Student Participants: David Witte*

David Witte, Cayley digraphs of prime-power order are hamiltonian, Journal of Combinatorial Theory, Series B, 11 (1987) 21-24.

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.

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.

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.

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 (1990) 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.

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.

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.

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.
Virgina Wright, n-Tuple vertex graphs, M.S. thesis Emory University, 1992.

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.

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.

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.
Stephen Curran and Joseph A. Gallian, Hamiltonian cycles and paths in Cayley graphs and digraphs--a survey, Discrete Mathematics , 156 (1996) 1-18.
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.

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.
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.

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, Electronic Journal of Combinatorics, 5 (1998), #R2, 11 pages.

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.

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*, (research adviser), 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.

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 W_n, 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.

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.

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, 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, to appear.
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.

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 , to appear.
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.

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 abeliansquare-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.

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 , to appear.
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.
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, to appear.
Ricky Liu, Counting subrings in Z^n of index k, Journal of Combinatorial Theory, Series A, 114 (2007) 278-299.
Jack Huizenga, Chromatic capacity and graph operations, Discrete Mathematics, to appear.
Karola Meszaros, On 3-regular 4-ordered graphs, Discrete Mathematics, to appear.
Karola Meszaros, On low degree k-ordered graphs, Discrete Mathematics, to appear.
Alexandra Ovetsky, On well-coveredness of Cartesian products of graphs, Discrete Mathematics, to appear.

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, On Wild semigroups, submitted.
Jacob Fox, A bipartite analogue of Dilworth's theorem, Order, (2006) 197-209.
Jack Huizenga, The maximum size of caps in (Z/nZ)².
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 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 , to appear.
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, to appear.
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.

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

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, to appear. Hannah Breckbill, Fixing numbers of hypercubesand hypercube variants, submitted.
Alan Deckelbaum,Minimum product set sizes in nonabelian groups of order pq, submitted.
Ariel Levavi, Tree pegging.
Maria Monks, The solution to the partition reconstruction problem, submitted.
Aaron Pixton, Alternators in the Cayley-Dickson algebras, Forum Mathematicum, to appear.
Aaron Pixton, Sequences with small subsum sets, submitted.