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

Contributions to Discrete Mathematics

Mircea Merca

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

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