A Fast Algorithm for MacMahon's Partition Analysis

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A Fast Algorithm for MacMahon's Partition Analysis
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.
Guoce Xin
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2004
Authors Guoce Xin
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