Combinatorial proofs of Ramanujan's 1 ψ 1 summation and the q-Gauss summation

Ae Ja Yee

doi:10.1016/j.jcta.2003.10.002

Combinatorial proofs of Ramanujan's 1 ψ ₁ summation and the q-Gauss summation

Ae Ja Yee

Mathematics

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

24 Scopus citations

Abstract

Theorems in the theory of partitions are closely related to basic hypergeometric series. Some identities arising in basic hypergeometric series can be interpreted in the theory of partitions using F-partitions. In this paper, Ramanujan's ₁ψ₁ summation and the q-Gauss summation are established combinatorially.

Original language	English (US)
Pages (from-to)	63-77
Number of pages	15
Journal	Journal of Combinatorial Theory. Series A
Volume	105
Issue number	1
DOIs	https://doi.org/10.1016/j.jcta.2003.10.002
State	Published - Jan 2004

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.2003.10.002

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abstract = "Theorems in the theory of partitions are closely related to basic hypergeometric series. Some identities arising in basic hypergeometric series can be interpreted in the theory of partitions using F-partitions. In this paper, Ramanujan's 1ψ1 summation and the q-Gauss summation are established combinatorially.",

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AB - Theorems in the theory of partitions are closely related to basic hypergeometric series. Some identities arising in basic hypergeometric series can be interpreted in the theory of partitions using F-partitions. In this paper, Ramanujan's 1ψ1 summation and the q-Gauss summation are established combinatorially.

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Combinatorial proofs of Ramanujan's 1 ψ ₁ summation and the q-Gauss summation

Abstract

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