|
Guoce Xin gxin@nankai.edu.cn guoce.xin@gmail.com http://www.combinatorics.net.cn/homepage/xin/ |
Center
for Combinatorics
|
o
Ph.D. in Mathematics, May
2004, at Brandeis University
advisor: Professor Ira M. Gessel,
thesis: the ring of Malcev-Neumann series and the
residue theorem.
o
Master in Mathematics, July
1997, at
advisor: Professor William Y.C.
Chen
o
Bachelor in Mathematics, July
1994, at
o
University of
o
Visiting Assistant Professor at
o
Visiting scholar at
o
Postdoctoral fellow at Institut
Mittag-Leffler, the Royal Swedish
o Center for Combinatorics, Nankai University, from May 2006 to now
o
Department of Mathematics,
o
Department of Mathematics,
l Research Interest
My primary research interest lies in the field of enumerate and algebraic combinatorics. One of my current plans is to develop more efficient algorithm for MacMahon’s Partition Analysis.
Ø with Guo-Niu Han, Permutations with Extremal number of Fixed Points, submitted, arXiv:0706.1738.
Ø with Lun Lv and Yue Zhou, A Family of $q$-Dyson Style Constant Term Identities, submitted, arXiv:0706.1009.
Ø with Ira Gessel, Lun Lv and Yue Zhou, Unified Elementary Approach to the Dyson, Morris, Aomoto, and Forrester Constant Terms, submitted, arXiv: math.CO/0701066.
Ø
with Richard Ehrenborg, Number of Standard Young Tableaux via Calculus!, in preparation.
1.
Partial fraction algorithm for
MacMahon’s partition analysis, Combinatorial
Seminar @ UCSD, August 16, 2007
2.
Enumeration of k-stacksortable
matchings and partitions, 2007 Permutation
Pattern conference @
3.
On Kronecker powers of
Schur functions of shape d,d, Combinatorial
Seminar @ University of
4.
A short proof of the
Zeilber-Bressoud q-Dyson Conjecture
5.
On MacMahon's partition analysis and
q-Dyson's conjecture, Additive Number Theory
Conference @ University of
6. MacMahon's partition analysis, Combinatorics Seminar @ MIT, October 6, 2004.
7. Lattice path enumerations, Graduate Seminar @ Brandeis University, March 16, 2004.
8. The ring of Malcev-Neumann series and the residue theorem, thesis defense @ Brandeis University, April 15, 2004.
o In the past years I have been working on different subjects, including plane walk and lattice path enumerations, residue theorem and constant term evaluations, patter-avoiding permutation problems, the study of super Catalan numbers, and continued fraction representations.
o My recent work focuses on combinatorial applications of Laurent series, which was developed in my thesis. I succeeded in applying this theory to
§ finding an algebraic proof of Zeilberger-Bressoud theorem, also called Andrew's q-Dyson's conjecture.
§ giving a fast algorithm for MacMahon's partition analysis.
§ proving Bousquet-Melou and Schaeffer's conjecture on slit plan walks.
§ proving a generalization of Richard Stanley's monster reciprocity theorem.
Last
updated: June 20, 2006
This homepage was set up on November 23, 2003