### Monday September 27, 2004

**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.