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

Authors

DOI:

https://doi.org/10.11575/cdm.v13i1.62505

Keywords:

integer partitions, partition congruences, recurrence relations

Abstract

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.

References

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Published

2018-01-29

Issue

Vol. 13 No. 1 (2018)

Section

Articles

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