Speaker: Guoce Xin (Brandeis)
Title: On MacMahon's Partition Analysis
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 quasi-polynomials. Recent results by (1998) G.E. Andrews and his co-authors, 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.