MacMahon's partition identity and the coin exchange problem

Ae Ja Yee

doi:10.1016/j.jcta.2009.02.006

MacMahon's partition identity and the coin exchange problem

Ae Ja Yee

Mathematics

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

2 Scopus citations

Abstract

One of MacMahon's partition theorems says that the number of partitions of n into parts divisible by 2 or 3 equals the number of partitions of n into parts with multiplicity larger than 1. Recently, Holroyd has obtained a generalization. In this short note, we provide a bijective proof of his theorem.

Original language	English (US)
Pages (from-to)	1228-1231
Number of pages	4
Journal	Journal of Combinatorial Theory. Series A
Volume	116
Issue number	7
DOIs	https://doi.org/10.1016/j.jcta.2009.02.006
State	Published - Oct 2009

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

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10.1016/j.jcta.2009.02.006

Cite this

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title = "MacMahon's partition identity and the coin exchange problem",

abstract = "One of MacMahon's partition theorems says that the number of partitions of n into parts divisible by 2 or 3 equals the number of partitions of n into parts with multiplicity larger than 1. Recently, Holroyd has obtained a generalization. In this short note, we provide a bijective proof of his theorem.",

author = "Yee, \{Ae Ja\}",

note = "Funding Information: Research partially supported by National Science Foundation Grant DMS-0801184. E-mail address: [email protected]. 1 The author is an Alfred P. Sloan Research Fellow.",

year = "2009",

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doi = "10.1016/j.jcta.2009.02.006",

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N1 - Funding Information: Research partially supported by National Science Foundation Grant DMS-0801184. E-mail address: [email protected]. 1 The author is an Alfred P. Sloan Research Fellow.

PY - 2009/10

Y1 - 2009/10

N2 - One of MacMahon's partition theorems says that the number of partitions of n into parts divisible by 2 or 3 equals the number of partitions of n into parts with multiplicity larger than 1. Recently, Holroyd has obtained a generalization. In this short note, we provide a bijective proof of his theorem.

AB - One of MacMahon's partition theorems says that the number of partitions of n into parts divisible by 2 or 3 equals the number of partitions of n into parts with multiplicity larger than 1. Recently, Holroyd has obtained a generalization. In this short note, we provide a bijective proof of his theorem.

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UR - https://www.scopus.com/pages/publications/67349119846#tab=citedBy

U2 - 10.1016/j.jcta.2009.02.006

DO - 10.1016/j.jcta.2009.02.006

M3 - Article

AN - SCOPUS:67349119846

SN - 0097-3165

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EP - 1231

JO - Journal of Combinatorial Theory. Series A

JF - Journal of Combinatorial Theory. Series A

IS - 7

ER -

MacMahon's partition identity and the coin exchange problem

Abstract

All Science Journal Classification (ASJC) codes

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