More infinite families of congruences modulo 5 for broken 2-diamond partitions

JOURNAL OF NUMBER THEORY

卷:170

Article

Xia, Ernest X. W.¹ 

[1] Jiangsu Univ, Dept Math, Zhenjiang 212013, Jiangsu, Peoples R China

关键词: Broken k-diamond partition;    Congruence;    Theta function;   

DOI  :  10.1016/j.jnt.2016.04.023

来源: Elsevier

【 摘 要 】

The notion of broken k-diamond partitions was introduced by Andrews and Paule. Let Delta(k)(n) denote the number of broken k-diamond partitions of n for a fixed positive integer k. Recently, Chan, and Paule and Radu proved some congruences modulo 5 for Delta(2)(n). In this paper, we prove several new infinite families of congruences modulo 5 for Delta(2)(n) by using an identity due to Newman. Our results generalize the congruences proved by Paule and Radu. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free