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arXiv · 2008.06401

General Congruences Modulo 5 and 7 for Colour Partitions

Nipen Saikia·Chayanika Boruah
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Abstract

For any positive integers $n$ and $r$, let $p_r(n)$ denotes the number of partitions of $n$ where each part has $r$ distinct colours. Many authors studied the partition function $p_r(n)$ for particular values of $r$. In this paper, we prove some general congruences modulo $5$ and $7$ for the colour partition function $p_r(n)$ by considering some general values of $r$. To prove the congruences we employ some $q$-series identities which is also in the spirit of Ramanujan.

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Nipen Saikia, Chayanika Boruah. 2020-08-14. General Congruences Modulo 5 and 7 for Colour Partitions. https://arxiv.org/abs/2008.06401

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