4-regular partitions and the pod function

Abstract

The function pod(n) enumerates the partitions of n wherein odd parts are distinct and even parts are unrestricted. Recently, a number of properties for pod(n) have been established. In this paper, we use connections with 4-regular partitions and, for fixed k ∈ {0, 2}, partitions into distinct parts not congruent to k modulo 4 in order to obtain new properties for pod(n). In this context, we derive two new infinite families of linear inequalities involving pod(n). We also obtain new identities of Watson type.