The combinatorics of MacMahon's partial fractions

Published 11 Dec 2018 in math.CO | (1812.04573v1)

Abstract: MacMahon showed that the generating function for partitions into at most $k$ parts can be decomposed into a partial fractions-type sum indexed by the partitions of $k$. In this present work, a generalization of MacMahon's result is given, which in turn provides a full combinatorial explanation.

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Andrew V. Sills

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