The combinatorics of MacMahon's partial fractions
Combinatorics
2019-12-23 v1
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.
Cite
@article{arxiv.1812.04573,
title = {The combinatorics of MacMahon's partial fractions},
author = {Andrew V. Sills},
journal= {arXiv preprint arXiv:1812.04573},
year = {2019}
}
Comments
12 pages. Full account of the author's plenary talk at Combinatory Analysis 2018: in Honor of George Andrews' 80th Birthday, June 24, 2018