Chayanika Boruah | Searcharxiv

arXiv2020

General Congruences Modulo 5 and 7 for Colour Partitions

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.

math.NT↗

arXiv2016

Some Congruences of a Restricted Bipartition Function

Let $c_N(n)$ denotes the number of bipartitions $(λ, μ)$ of a positive integer $n$ subject to the restriction that each part of $μ$ is divisible by $N$. In this paper, we prove some congruence properties of the function $c_N(n)$ for $N=7$, 11, and $5l$, for any integer $l\ge 1$, by employing Ramanujan's theta-function identities.

math.NT↗