#### Vol. 4, No. 4, 2011

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Congruence properties of $S$-partition functions

### Andrew Gruet, Linzhi Wang, Katherine Yu and Jiangang Zeng

Vol. 4 (2011), No. 4, 411–416
##### Abstract

We study the function $p\left(S;n\right)$ that counts the number of partitions of $n$ with elements in $S$, where $S$ is a set of integers. Generalizing previous work of Kronholm, we find that given a positive integer $m$, the coefficients of the generating function of $p\left(S;n\right)$ are periodic modulo $m$, and we use this periodicity to obtain families of $S$-partition congruences. In particular, we obtain families of congruences between partition functions $p\left({S}_{1};n\right)$ and $p\left({S}_{2};n\right)$.

##### Keywords
Brandt Kronholm, Ramanujan-type congruences, S-partition functions
Primary: 11P83