Some congruences for e-regular partitions with certain restrictions

Let pod (n) and ped, (n) denote the number of f-regular partitions of a positive integer n into distinct odd parts and the number of e-regular partitions of a positive integer n into distinct even parts, respectively. Our first goal in this note was to prove two congruence relations for pod (n). Furthermore, we found a formula for the action of the Hecke operator on a class of eta-quotients. As two applications of this result, we obtained two infinite families of congruence relations for pods(n). We also proved a congruence relation for ped, (n). In particular, we established a congruence relation modulo 2 connecting pod (n) and ped, (n).