Arithmetic of 2-regular partitions with distinct odd parts

Abstract

Let $po{d}_2(n)$ denote the number of $2$-regular partitions of $n$ with distinct odd parts (even parts are unrestricted). In this article, we obtain congruences for $po{d}_2(n)$ mod $2$ and mod $8$ using some generating function manipulations and the theory of Hecke eigenform.

8 pages