Two partition functions with congruences modulo 3, 5, 7, and 13

Chris Jennings-Shaffer

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arXiv · 1505.06467

Two partition functions with congruences modulo 3, 5, 7, and 13

Chris Jennings-Shaffer

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Abstract

We introduce two new integer partition functions, both of which are the number of partition quadruples of $n$ with certain size restrictions. We prove both functions satisfy Ramanujan-type congruences modulo $3$, $5$, $7$, and $13$ by use of generalized Lambert series identities and $q$-series techniques.

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Chris Jennings-Shaffer. 2016-03-18. Two partition functions with congruences modulo 3, 5, 7, and 13. https://arxiv.org/abs/1505.06467

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