A Partition Bijection Related to the Rogers-Selberg Identities and Gordon's Theorem

Andrew V. Sills

doi:j.jcta.2007.04.001

A Partition Bijection Related to the Rogers-Selberg Identities and Gordon's Theorem

Andrew V. Sills

Mathematical Sciences

Georgia Southern University

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

3 Scopus citations

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	American English
Journal	Journal of Combinatorial Theory, Series A
Volume	115
DOIs	https://doi.org/j.jcta.2007.04.001
State	Published - Jan 1 2008

Keywords

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

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Mathematics

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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 - Rogers-Ramanujan identities

KW - Rogers-Selberg identities

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A Partition Bijection Related to the Rogers-Selberg Identities and Gordon's Theorem

Abstract

Keywords

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