| My research interests are mostly in algebraic combinatorics. Lately I have been studying the Shuffle conjecture and the structure coefficients of the k-Schur functions of Lapointe/Lascoux/Morse. |
Published papers |
| A Macdonald Vertex Operator and Tableaux Statistics for the Two-Column (q,t)-Kostka Coefficients, Electronic Journal of Combinatorics, 5, R45, (extended abstract) |
| Vertex operators for standard bases of the symmetric functions, J. of Alg. Comb., 13, No. 1 (2000), pp. 83-101. (math.CO/9904084) |
| Positivity for special cases of (q,t)-Kostka coefficients and standard tableaux statistics, Electronic Journal of Combinatorics, 6, R41 |
| (with Mark Shimozono) Hall-Littlewood vertex operators and generalized Kostka polynomials, Adv. in Math., 158 (2001), pp. 66-85. (math.QA/0001168) |
| Ribbon Operators and Hall-Littlewood Symmetric Functions, Adv. in Math., 156 (2000), pp. 33-43. (math.QA/0008163) (extended abstract) |
| (with Adriano Garsia) Polynomiality of the q,t-Kostka Revisited, Algebraic combinatorics and computer science, Springer Italia, Milan, (2001), pp. 473-491. (math.QA/0008199) |
| q-Analogs of symmetric function operators, Disc. Math., 256 (2002), pp. 831-853. (math.QA/0008188) |
| (with N. Bergeron) q and q,t-Analogs of Non-commutative Symmetric Functions, Discrete Mathematics, 298, 1, (2005), pp. 79-103. (math.CO/0106255) |
| (with G. Tudose) q-Analogs of Q-Schur functions, Algebraic Combinatorics and Quantum Groups, Nihuan Jing, ed., World Sci. Publ., 2003. (math.CO/0203046) (extended abstract) |
| (with C. De Concini, C. Procesi, E. Rogora) On Equations of Degree 3 * 2^m, Boletin del Instituto de Matematica ``Beppo Levi,'' Vol II, Rosario, Argentina, (2003/4), pp. 109-122. (pdf version) |
| (with M. Shimozono) Deformed universal characters for classical and affine algebras, Journal of Algebra, 299 (2006), pp. 33-61, (math.CO/0404288) (extended abstract) |
| (with M. H. Albert, M. Elder, A. Rechnitzer, P. Westcott) On the Wilf-Stanley limit of 4231-avoiding permutations and a conjecture of Arratia, Adv. in Applied Mathematics, 36, 2, (2006), pp. 96-105. (math.CO/0502504) |
| (with N. Bergeron, C. Hohwleg) Posets related to the connectivity set of Coxeter groups, J. of Alg., 303, 2, (2006), pp. 831-846, (math.CO/0509271). |
| (with N. Bergeron, C. Hohwleg, and M. Rosas) Grothendieck bialgebras, Partition lattices and symmetric functions in noncommutative variables, Electr. J. of Comb., R75, Volume 13(1), 2006, 19 pages. |
| (with N. Bergeron, C. Reutenauer, M. Rosas) Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables, Canadian Math Journal (2008), Vol 60, No 2, pp. 266-296. (math.CO/0502082) |
| (with E. Briand, M. Rosas) On the S_n-module structure of the noncommutative harmonics, Journal of Combinatorial Theory, Series A, Volume 115, Issue 6, August 2008, pages 1077-1085. (0704.1101) |
| (with A. Garsia, N. Wallach, G. Xin) Hilbert Series of Invariants, Constant terms and Kostka-Foulkes Polynomials, Discrete Mathematics, Volume 309, Issue 16, pp. 5206-5230 (2009). (pdf version) |
| (with N. Bergeron, F. Descouens) A non-commutative generalization of $k$-Schur functions, Discrete Mathematics, Volume 309, Issue 16, pp. 5092-5105 (2009). (0804.0944v1) |
| (with N. Bergeron, F. Descouens) A Filtration of (q,t)-Catalan numbers, Advances in Applied Mathematics 44 pp. 1636 (2010) . (arXiv:0806.3046) |
| (with N. Bergeron) The Hopf algebras of symmetric functions and quasi-symmetric functions in non-commutative variables are free and cofree, J. of Alg. and Its Appl., Volume: 8 (4), pp. 581-600 (2009) . (math.CO/0509265) |
| (with A. Brown, S. van Willigenburg) Expressions for Catalan Kronecker Products, Pacific Journal of Mathematics, Vol. 248 (2010), No. 1, 31-48. (arxiv:0809.3469) |
| (with J. Bandlow and A. Schilling) The Murnaghan-Nakayama Rule for k-Schur Functions, Journal of Combinatorial Theory, Series A Volume 118, Issue 5, June 2011, pp. 1588-1607, (arXiv:1004.4886) |
| (with A. Garsia and G. Xin) Hall-Littlewood Operators
in the Theory of Parking Functions and Diagonal Harmonics,
International Mathematics Research Notices 2011;
doi: 10.1093/imrn/rnr060 |
| (with J. Haglund and J. Morse) A compositional shuffle conjecture specifying touch points of the Dyck path, (arXiv:1008.0828v2), to appear Candian Journal Mathematics. |
| (with Marcelo Aguiar, Carlos Andre, Carolina Benedetti, Nantel Bergeron, Zhi Chen, Persi Diaconis, Anders Hendrickson, Samuel Hsiao, I. Martin Isaacs, Andrea Jedwab, Kenneth Johnson, Gizem Karaali, Aaron Lauve, Tung Le, Stephen Lewis, Huilan Li, Kay Magaard, Eric Marberg, Jean-Christophe Novelli, Amy Pang, Franco Saliola, Lenny Tevlin, Jean-Yves Thibon, Nathaniel Thiem, Vidya Venkateswaran, C. Ryan Vinroot, Ning Yan) Supercharacters, symmetric functions in noncommuting variables, and related Hopf algebras (arXiv:1009.4134), Advances in Mathematics, Volume 229, Issue 4, 1 March 2012, Pages 2310--2337. |
| (with A. Bergeron-Brlek and C. Hohlweg) Words and polynomial invariants of finite groups in non-commutative variables, (arXiv:0907.0814), Annals of Combinatorics, DOI: 10.1007/s00026-011-0119-0. |
| (with A. Garsia, N. Wallach, G. Xin) Kronecker Coefficients via Symmetric Functions and Constant Term identities, (pdf version), to appear IJAC. |
Other Papers/Projects/Drafts/Submissions |
| (with Rosa Orellana) Some remarks on the characters of the general Lie superalgebra, (math.CO/0008152) | A Bijective Proof of an Unusual Symmetric Group Generating Function (math.CO/0310301) |
| (with M. Mishna, draft) Analytic aspects of the shuffle product, Dans Proceedings of the 25th Annual Symposium on the Theoretical Aspects of Computer Science - STACS 2008, Bordeaux : France (2008) (arXiv:0802.2844) |
| (with C. Berg, N. Bergeron and H. Thomas) Expansion of $k$-Schur functions for maximal $k$-rectangles within the affine nilCoxeter algebra, submitted (arxiv:1107.3610). |
| (with A. M. Garsia, G. Xin) Proof of the 2-part Compositional Shuffle Conjecture, draft. |
| (with A. Garsia and G. Xin) On a three part case of the Shuffle Conjecture, draft. |
| (with C. Berg) Symmetries of the $k$-bounded partition lattice, (arxiv:1111.2783v2). |
| (with A. Schilling, J. Morse, L. Lapointe) A Primer on $k$-Schur functions, draft. |
| (with A. Duane and A. Garsia) A new dinv Arising from the Two Part Case of the Shuffle Conjecture, draft. |
| Sequences from The On-Line Encyclopedia of Integer Sequences |
Talks and posters |
| PDF of slides for talk "q-Analogs of Hopf Algebra Structures" given in Kyoto Aug '01 |
| PDF of poster presented at FPSAC'01 in Scottsdale, Arizona June '01 "The ribbon rule for homogeneous symmetric functions" (extended abstract) |
| PDF of slides for talk "A quantization of non-commutative symmetric functions" at the CMS Winter meeting '01 and updated for a seminar at UWaterloo June, '02. This is similar to the chalk talk that I presented at several combinatorics seminars (York, UMinnesota, UQaM) Fall '01. |
| PDF of slides "Ribbons and Column Strict Tableaux" presented at the Univeristy of Miami and York University colloquium Feb '02. |
| PDF of slides "A q-analog of Schur's Q-functions" presented at the Wilfrid Laurier University April '02. Description of this research. |
| FPSAC '02. "Hall-Littlewood analogs in the Q-function algebra" (PDF slides) and "q and qt analogs of non-commutative symmetric functions." (PDF slides) |
| Prof Talk- for Club Infinity at York University. "Gems of algebra: The secret life of the symmetric group" (PDF of slides) |
| A Java program to play a game of extended "Set." I learned a lot about the work that has been done on the game of "Set" at the FPSAC '01 conference where I gave a demo of this program, but I have not had the chance to rewrite the material on the web page to reflect that. |
| A gallery of posets. Pictures of permutahedron and other geometric shapes arising from posets. |
|
A series of three talks on symmetric functions in non-commuting
variables
that I gave in Rome, December 2006 for the
Incontro
Italiano di Combinatoria Algebrica. A zoo of Hopf algebras Combinatorics and coinvariants A representation theoretical approach |
|
Slides from two talks that I gave at the meeting
Combinatorial Algebra meets Algebraic Combinatorics. A (nother version of the) zoo of Hopf algebras The wilderness of Hopf algebras |
|
Presentation that I gave at Wake Forest University (updated from the one that I gave at
the Fields Institute) k-Schur functions indexed by a maximal rectangle |