General Congruences Modulo 5 and 7 for Colour Partitions

Nipen Saikia; Chayanika Boruah

paper

General Congruences Modulo 5 and 7 for Colour Partitions

arXiv:2008.06401

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.

10 Pages