Guoce Xin

Center for Combinatorics
Nankai University
Tianjin 300071
P.R. China

Tel: +86-22-2350-5133 (ext: 8024)              Fax:+86-22-2350-9272

l         Education

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 Nankai University
        advisor: Professor William Y.C. Chen

o        Bachelor in Mathematics, July 1994,  at Nankai University

l         Research Experience

o        University of California, San Diego, March and May, 2006, invited by Professor Adriano Garsia for short term cooperation.

o        Visiting Assistant Professor at University of Kentucky, from Aug. 2005 to May 2006.

o        Visiting scholar at Institute of Mathematics, Academia Sinica, Taiwan, from May to June 2005, invited by I-Chiau Huang.

o        Postdoctoral fellow at Institut Mittag-Leffler, the Royal Swedish Academy of Sciences, Sweden, from Feb. to May 2005.

l         Employment

o        Center for Combinatorics, Nankai University, from May 2006 to now

o        Department of Mathematics, University of Kentucky, from Aug. 2005 to May 2006

o        Department of Mathematics, Tianjin University, from Oct. 1997 to June 1999

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.

l         Publications

l         Preprints

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.

l         Selected Talk Slides

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 @ St. Andrews, June 14, 2007

3.          On Kronecker powers of Schur functions of shape d,d, Combinatorial Seminar @ University of Kentucky, April 26, 2006

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 Florida, November 20, 2004.

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