Ramanujan-type Congruences for ℓ-Regular Partitions Modulo 3, 5, 11 and 13

2015/09/25 by Jin, Hai-Tao, Zhang, Li
#05A17 #11P83 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1509.07591

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 b₁₁(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.

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