Ramanujan-type congruences for ℓ-regular partitions modulo 3, 5, 11 and 13

Abstract

Let b ℓ (n) be the number of ℓ-regular partitions of n. Recently, Hou et al established several infinite families of congruences for b ℓ (n) modulo m, where (ℓ, m) = (3, 3), (6, 3), (5, 5), (10, 5) and (7, 7). In this paper, by the vanishing property given by Hou et al, we show an infinite family of congruence for b 11 (n) modulo 11. Moreover, for ℓ = 3, 13 and 25, we obtain three infinite families of congruences for b ℓ (n) modulo 3, 5 and 13 by the theory of Hecke eigenforms.