The Combinatorics of MacMahon’s Partial Fractions

Andrew V. Sills

doi:10.1007/s00026-019-00460-9

The Combinatorics of MacMahon’s Partial Fractions

Andrew V. Sills

Mathematical Sciences

Georgia Southern University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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

Original language	English
Pages (from-to)	1073-1086
Number of pages	14
Journal	Annals of Combinatorics
Volume	23
Issue number	3-4
DOIs	https://doi.org/10.1007/s00026-019-00460-9
State	Published - Nov 1 2019

Scopus Subject Areas

Discrete Mathematics and Combinatorics

Keywords

Compositions
Partition function
Partitions
Symmetric group

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10.1007/s00026-019-00460-9

Cite this

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title = "The Combinatorics of MacMahon{\textquoteright}s Partial Fractions",

abstract = "MacMahon showed that the generating function for partitions into at most k parts can be decomposed into a partial fraction-type sum indexed by the partitions of k. In the present work, a generalization of MacMahon{\textquoteright}s result is given, which in turn provides a full combinatorial explanation.",

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

KW - Compositions

KW - Partition function

KW - Partitions

KW - Symmetric group

UR - https://www.scopus.com/pages/publications/85074838297

U2 - 10.1007/s00026-019-00460-9

DO - 10.1007/s00026-019-00460-9

M3 - Article

AN - SCOPUS:85074838297

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VL - 23

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JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 3-4

ER -

The Combinatorics of MacMahon’s Partial Fractions

Abstract

Scopus Subject Areas

Keywords

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