Arithmetic Properties of Partition k-tuples with Odd Parts Distinct

摘要

Let pod-k(n) denote the number of partition k-tuples of n wherein odd parts are distinct (and even parts are unrestricted). We establish some interesting infinite families of congruences and internal congruences modulo 4, 16, and 5 for pod-2(n), pod-4(n), and pod-6(n), respectively. We also find Ramanujan-type congruences modulo 5 for pod-3(n) and densities of pod-2(n), pod-3(n), pod-4(n), and pod-6(n) modulo 4, 5, 16, and 5, respectively.