On the number of partitions into odd parts or congruent to $pm 2 pmod{10}$

Contributions to Discrete Mathematics

Mircea Merca¹ 

[1] Academy of Romanian Scientists

关键词: integer partitions;    partition congruences;    recurrence relations;   

DOI  :  10.11575/cdm.v13i1.62505

学科分类：社会科学、人文和艺术（综合）

来源: University of Calgary * Department of Mathematics and Statistics

【 摘 要 】

Let $R_2(n)$ denote the number of partitions of $n$ into parts that are odd or congruent to $pm 2 pmod{10}$. In 2007, Andrews considered partitions with some negative parts and provided a second combinatorial interpretation for $R_2(n)$. In this paper, we give a collection of linear recurrence relations for the partition function $R_2(n)$. As a corollary, we obtain a simple criterion for deciding whether $R_2(n)$ is odd or even. Some identities involving overpartitions and partitions into distinct parts are derived in this context.

【 授权许可】

Unknown