Arithmetic of 2-regular partitions with distinct odd parts

Hemjyoti Nath

Published 2024-08-25Version 1

Let $pod_2(n)$ denote the number of $2$-regular partitions of $n$ with distinct odd parts (even parts are unrestricted). In this article, we obtain congruences for $pod_2(n)$ mod $2$ and mod $8$ using some generating function manipulations and the theory of Hecke eigenform.