Affiliation: Brandeis University
Email: maxima@brandeis.edu
Title Of Talk: On MacMahon's partition analysis
URLS:
front.math.ucdavis.edu/math.CO/0408377
front.math.ucdavis.edu/math.CO/0409468
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. G.E. Andrews and his co-authors (1998), introduces the Omega package to solve such problems using computer, and gives a new life to this subject. I will in this talk 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" (published by Electron. J. Combin., 11(2004) arXiv: math.CO/0408377).
Last update made Thu Nov 11 14:47:25 EST 2004.
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