Arithmetic properties of partition triples with odd parts distinct

Abstract

Let pod -3(n) denote the number of partition triples of n where the odd parts in each partition are distinct. We find many arithmetic properties of pod -3(n) involving the following infinite family of congruences: for any integers α ≥ 1 and n ≥ 0, [Formula: see text] We also establish some arithmetic relations between pod (n) and pod -3(n), as well as some congruences for pod -3(n) modulo 7 and 11.