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arXiv · 1408.5061

Congruences for Partition Pairs with Conditions

Chris Jennings-Shaffer
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Abstract

We prove congruences for the number of partition pairs $(\pi_1,\pi_2)$ such that $\pi_1$ is non-empty, $s(\pi_1)\le s(\pi_2)$, and $\ell(\pi_2)< 2s(\pi_1)$ where $s(\pi)$ is the smallest part and $\ell(\pi)$ is the largest part of a partition. The proofs use Bailey's Lemma and a generalized Lambert series identity of Chan. We also discuss how a partition pair crank gives combinatorial refinements of these congruences.

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Chris Jennings-Shaffer. 2014-08-21. Congruences for Partition Pairs with Conditions. https://arxiv.org/abs/1408.5061

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