New analogues of Ramanujan's partition identities

“…There are many similar properties between a(n) and the standard partition function p(n), see [5][6][7][8][9]11] for examples. One of the nice results of a(n) is the generating function of a(3n + 2) obtained by Chan [5], which states that ∞ n=0 a(3n + 2)q n = 3 (q 3 ; q 3 ) 3 ∞ (q 6 ; q 6 ) 3 ∞ (q; q) 4 ∞ (q 2 ; q 2 ) 4…”

Section: Introductionmentioning

confidence: 99%

Ramanujan Type Congruences for a Partition Function

Zhao¹,

Zhong²

2011

Electron. J. Combin.

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“…Chan and Toh [7] also established the following nice congruence, which was also discovered by Xiong [20] independently.…”

Section: Introductionmentioning

confidence: 55%

Arithmetic Properties of a Restricted Bipartition Function

Liu

Wang

2015

Electron. J. Combin.

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A bipartition of $n$ is an ordered pair of partitions $(\lambda,\mu)$ such that the sum of all of the parts equals $n$. In this article, we concentrate on the function $c_5(n)$, which counts the number of bipartitions $(\lambda,\mu)$ of $n$ subject to the restriction that each part of $\mu$ is divisible by $5$. We explicitly establish four Ramanujan type congruences and several infinite families of congruences for $c_5(n)$ modulo $3$.

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New analogues of Ramanujan's partition identities

Abstract: We establish several new analogues of Ramanujan's exact partition identities using the theory of modular functions.

Cited by 48 publications

References 13 publications

Multiranks and classical theta functions

Multiranks and classical theta functions

Ramanujan Type Congruences for a Partition Function

Arithmetic Properties of a Restricted Bipartition Function

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