Congruences for 13-regular partitions - Cui, Su-Ping; Gu, Nancy S.S. (Utilitas Mathematica, 2018)
A partition is called ℓ -regular partition if there is no part divisible by ℓ. Let bℓ (n) denote the number of ℓ -regular partitions of n. The divisibility and distribution of b ℓ (n) have been widely studied in the literature. In this paper, we mainly focus on congruences for the 13-regular partition function. By means of Jacobi's identity and the modular equations of fifth and seventh order, we derive new infinite families of congruences for b13(n) modulo 13. Meanwhile, in view of a congruence relation for b13(n) given by Calkin et al. and some congruences for b4(n), we obtain further congruences for b13(n) modulo 2. © 2018 Utilitas Mathematica Publishing Inc. All rights reserved.