A partition bijection related to the Rogers-Selberg identities and Gordon's theorem

Andrew V. Sills

doi:10.1016/j.jcta.2007.04.001

A partition bijection related to the Rogers-Selberg identities and Gordon's theorem

Andrew V. Sills

Mathematical Sciences

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Abstract

We provide a bijective map from the partitions enumerated by the series side of the Rogers-Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon's combinatorial generalization of the Rogers-Ramanujan identities. The implications of applying the same map to a special case of David Bressoud's even modulus analog of Gordon's theorem are also explored.

Original language	English
Pages (from-to)	67-83
Number of pages	17
Journal	Journal of Combinatorial Theory, Series A
Volume	115
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2007.04.001
State	Published - Jan 2008

Scopus Subject Areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Keywords

Andrews-Gordon-Bressoud theorem
Gordon's theorem
Partitions
Rogers-Ramanujan identities
Rogers-Selberg identities

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10.1016/j.jcta.2007.04.001

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abstract = "We provide a bijective map from the partitions enumerated by the series side of the Rogers-Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon's combinatorial generalization of the Rogers-Ramanujan identities. The implications of applying the same map to a special case of David Bressoud's even modulus analog of Gordon's theorem are also explored.",

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AB - We provide a bijective map from the partitions enumerated by the series side of the Rogers-Selberg mod 7 identities onto partitions associated with a special case of Basil Gordon's combinatorial generalization of the Rogers-Ramanujan identities. The implications of applying the same map to a special case of David Bressoud's even modulus analog of Gordon's theorem are also explored.

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KW - Gordon's theorem

KW - Partitions

KW - Rogers-Ramanujan identities

KW - Rogers-Selberg identities

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DO - 10.1016/j.jcta.2007.04.001

M3 - Article

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JO - Journal of Combinatorial Theory, Series A

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A partition bijection related to the Rogers-Selberg identities and Gordon's theorem

Abstract

Scopus Subject Areas

Keywords

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