Bijective proofs of partition identities of MacMahon, Andrews, and Subbarao

Shishuo Fu; James Allen Sellers

doi:10.37236/3907

Bijective proofs of partition identities of MacMahon, Andrews, and Subbarao

Shishuo Fu
, James Allen Sellers

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

7 Scopus citations

Abstract

We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to 2,3,4,6(mod6), together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result.

Original language	English (US)
Journal	Electronic Journal of Combinatorics
Volume	21
Issue number	2
DOIs	https://doi.org/10.37236/3907
State	Published - May 28 2014
Externally published	Yes

Keywords

Bijection
Generating function
Partition
Residue classes

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10.37236/3907

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abstract = "We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to 2,3,4,6(mod6), together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result.",

keywords = "Bijection, Generating function, Partition, Residue classes",

author = "Shishuo Fu and Sellers, \{James Allen\}",

year = "2014",

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AU - Sellers, James Allen

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N2 - We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to 2,3,4,6(mod6), together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result.

AB - We revisit a classic partition theorem due to MacMahon that relates partitions with all parts repeated at least once and partitions with parts congruent to 2,3,4,6(mod6), together with a generalization by Andrews and two others by Subbarao. Then we develop a unified bijective proof for all four theorems involved, and obtain a natural further generalization as a result.

KW - Bijection

KW - Generating function

KW - Partition

KW - Residue classes

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ER -

Bijective proofs of partition identities of MacMahon, Andrews, and Subbarao

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