| Abstrakt: |
Let p o d ℓ (n) and p e d ℓ (n) denote the number of ℓ -regular partitions of a positive integer n into distinct odd parts and the number of ℓ -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 p o d ℓ (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 p o d 5 (n) . We also proved a congruence relation for p e d ℓ (n) . In particular, we established a congruence relation modulo 2 connecting p o d ℓ (n) and p e d ℓ (n) . [ABSTRACT FROM AUTHOR] |
