The combinatorics of MacMahon's partial fractions
arXiv:1812.04573 · doi:10.1007/s00026-019-00460-9
Abstract
MacMahon showed that the generating function for partitions into at most parts can be decomposed into a partial fractions-type sum indexed by the partitions of . In this present work, a generalization of MacMahon's result is given, which in turn provides a full combinatorial explanation.
12 pages. Full account of the author's plenary talk at Combinatory Analysis 2018: in Honor of George Andrews' 80th Birthday, June 24, 2018