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 MalcevNeumann 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
MittagLeffler, 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 GuoNiu 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 kstacksortable
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
ZeilberBressoud qDyson Conjecture
5.
On MacMahon's partition analysis and
qDyson'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 MalcevNeumann 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, patteravoiding 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 ZeilbergerBressoud theorem, also called Andrew's qDyson's conjecture.
§ giving a fast algorithm for MacMahon's partition analysis.
§ proving BousquetMelou 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