@article{Yu2024, 
author = {JingJun Yu},
title = {Some congruences for    ℓ-regular partitions with certain restrictions},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {3},
pages = {6368-6378},
keywords = {congruences, partitions, Hecke operator},
url = {https://www.sciopen.com/article/10.3934/math.2024310},
doi = {10.3934/math.2024310},
abstract = {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  ).}
}