Congruences for the number of partitions and bipartitions with distinct even parts

Abstract

Let $ped(n)$ denote the number of partitions of $n$ wherein even parts are distinct (and odd parts are unrestricted). We show infinite families of congruences for $ped(n)$ modulo $8$. We also examine the behavior of $pe{d}_{-2}(n)$ modulo $8$ in detail where $pe{d}_{-2}(n)$ denotes the number of bipartitions of $n$ with even parts distinct. As a result, we find infinite families of congruences for $pe{d}_2(n)$ modulo $8$.