MIT Combinatorics Seminar
On MacMahon's partition analysis
Guoce Xin
(Brandeis University)
http://people.brandeis.edu/~maxima/
Wednesday, October 06, 2004
4:15 pm Room 2338
ABSTRACT

In his famous book "Combinatory Analysis" MacMahon introduced
partition analysis as a computational method for solving problems of
counting solutions to linear Diophantine equations and inequalities,
counting lattice points in a convex polytope, and computing Ehrhart
quasipolynomials. Recent results by (1998) G.E. Andrews and his
coauthors, together with their Omega package, which can be used
as a tool for solving such problems, will be introduced. I will present
a new approach, which combines the theory of iterated Laurent series
and a new algorithm for partial fraction decompositions, and leads to
an algorithm, whose running time is much less than that of the Omega
package.
This talk is going to be mostly based on my paper, "A Fast Algorithm
for MacMahon's Partition Analysis" (accepted by Electron. J. Combin.,
arXiv: math.CO/0408377).


