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

3 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

Keywords

Compositions
Partition function
Partitions
Symmetric group

Access to Document

10.1007/s00026-019-00460-9

Cite this

@article{323370a5833747578a32b89fa842d694,

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.",

keywords = "Compositions, Partition function, Partitions, Symmetric group",

author = "Sills, {Andrew V.}",

note = "Publisher Copyright: {\textcopyright} 2019, Springer Nature Switzerland AG.",

year = "2019",

month = nov,

day = "1",

doi = "10.1007/s00026-019-00460-9",

language = "English",

volume = "23",

pages = "1073--1086",

journal = "Annals of Combinatorics",

issn = "0218-0006",

publisher = "Birkhauser Verlag Basel",

number = "3-4",

}

TY - JOUR

T1 - The Combinatorics of MacMahon’s Partial Fractions

AU - Sills, Andrew V.

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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.

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 - http://www.scopus.com/inward/record.url?scp=85074838297&partnerID=8YFLogxK

U2 - 10.1007/s00026-019-00460-9

DO - 10.1007/s00026-019-00460-9

M3 - Article

AN - SCOPUS:85074838297

SN - 0218-0006

VL - 23

SP - 1073

EP - 1086

JO - Annals of Combinatorics

JF - Annals of Combinatorics

IS - 3-4

ER -

The Combinatorics of MacMahon’s Partial Fractions

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this