|
Guoce Xin gxin@nankai.edu.cn guoce.xin@gmail.com http://www.combinatorics.net.cn/homepage/xin/ |
Center for
|
o
Ph.D. in Mathematics, May
2004, at
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,
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 Constructing all magic squares of order three, submitted, arXiv: math.CO/0409468.
Ø A generalization of Stanley's Monster Reciprocity Theorem, submitted, arXiv: math.CO/0504425.
Ø
with Richard Ehrenborg, Number of Standard Young Tableux via Calculus!, in preparation.
1.
On Kronecker powers of
Schur functions of shape d,d, Combinatorial
Seminar @ University of
2.
A short proof of the
Zeilber-Bressoud q-Dyson Conjecture
3.
On MacMahon's partition analysis and q-Dyson's
conjecture, Additive Number Theory Conference @
University of
4. MacMahon's partition analysis, Combinatorics Seminar @ MIT, October 6, 2004.
5. Lattice path enumerations, Graduate Seminar @ Brandeis University, March 16, 2004.
6. 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