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arXiv · 1511.00246

New congruences for 2-color partitions

Shane Chern
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Abstract

Let $p_k(n)$ denote the number of $2$-color partitions of $n$ where one of the colors appears only in parts that are multiples of $k$. We will prove a conjecture of Ahmed, Baruah, and Dastidar on congruences modulo $5$ for $p_k(n)$. Moreover, we will present some new congruences modulo $7$ for $p_4(n)$.

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Shane Chern. 2016-02-09. New congruences for 2-color partitions. https://doi.org/10.1016/j.jnt.2015.12.020

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