A Fast Algorithm for MacMahon's Partition Analysis
Combinatorics
2007-05-23 v1
Abstract
This paper deals with evaluating constant terms of a special class of rational functions, the Elliott-rational functions. The constant term of such a function can be read off immediately from its partial fraction decomposition. We combine the theory of iterated Laurent series and a new algorithm for partial fraction decompositions to obtain a fast algorithm for MacMahon's Omega calculus, which (partially) avoids the "run-time explosion" problem when eliminating several variables. We discuss the efficiency of our algorithm by investigating problems studied by Andrews and his coauthors; our running time is much less than that of their Omega package.
Cite
@article{arxiv.math/0408377,
title = {A Fast Algorithm for MacMahon's Partition Analysis},
author = {Guoce Xin},
journal= {arXiv preprint arXiv:math/0408377},
year = {2007}
}
Comments
22 pages