Some congruences modulo 3, 5 and 7 for broken ((rl-1)/2)-diamond partitions for r ∈ {3,25,49} and odd positive integer l

被引：0

作者：

Saikia, Nipen ^{[1
]}

Chetry, Jubaraj ^{[1
]}

机构：

[1] Rajiv Gandhi Univ, Dept Math, Rono Hills, Doimukh 791112, Arunachal Prade, India

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 460卷 / 02期

关键词：

Broken k-diamond partition; Partition congruence; q-Identities; K-DIAMOND PARTITIONS; 3-DIAMOND PARTITIONS; SIMPLE PROOF; PARITY; ANDREWS; POWERS;

D O I：

10.1016/j.jmaa.2017.12.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For any non negative integer n and a fixed positive integer k, let Delta(k)(n) denote the number of broken k-diamond partitions of n. In this paper, we prove some congruences modulo 3 for Delta((3l-1)/2)(n), modulo 5 for Delta((25l-1)/2)(n), and modulo 7 for Delta((49l-1)/2)(n), for odd positive integer l. We also prove a new congruence modulo 5 for Delta(2)(n). (C) 2017 Elsevier Inc. All rights reserved.

引用

页码：645 / 655

页数：11

共 19 条

[1] MacMahon's partition analysis XI: Broken diamonds and modular forms [J].