New congruences modulo 5 for the number of 2-color partitions

JOURNAL OF NUMBER THEORY

卷:157

Article

Ahmed, Zakir¹  Baruah, Nayandeep Deka¹  Dastidar, Manosij Ghosh² 

[1] Tezpur Univ, Dept Math Sci, Sonitpur 784028, Assam, India

[2] Pondicherry Univ, Dept Math Sci, Kalapet 605014, Puducherry, India

关键词: Partitions;    2-Color partitions;    Partition congruences;   

DOI  :  10.1016/j.jnt.2015.05.002

来源: Elsevier

【 摘 要 】

Let p(k)(n) be the number of 2-color partitions of n where one of the colors appears only in parts that are multiples of k. In this paper, we find some interesting congruences modulo 5 for p(k)(n) for k is an element of {2, 3, 4} by employing Ramanujan's theta function identities and some identities for the Rogers Ramanujan continued fraction. The congruence for p(2)(n) was earlier proved by Chen and Lin with the aid of modular forms. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free