## Involve: A Journal of Mathematics

• Involve
• Volume 4, Number 4 (2011), 411-416.

### Congruence properties of $S$-partition functions

#### Abstract

We study the function $p(S;n)$ 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 $p(S;n)$ 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 $p(S1;n)$ and $p(S2;n)$.

#### Article information

Source
Involve, Volume 4, Number 4 (2011), 411-416.

Dates
Accepted: 17 June 2011
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.involve/1513733433

Digital Object Identifier
doi:10.2140/involve.2011.4.411

Mathematical Reviews number (MathSciNet)
MR2905237

Zentralblatt MATH identifier
1279.11103

Subjects
Primary: 11P83: Partitions; congruences and congruential restrictions

#### Citation

Gruet, Andrew; Wang, Linzhi; Yu, Katherine; Zeng, Jiangang. Congruence properties of $S$-partition functions. Involve 4 (2011), no. 4, 411--416. doi:10.2140/involve.2011.4.411. https://projecteuclid.org/euclid.involve/1513733433

#### References

• B. Kronholm, “On congruence properties of $p(n,m)$”, Proc. Amer. Math. Soc. 133:10 (2005), 2891–2895.
• B. Kronholm, “On congruence properties of consecutive values of $p(n,m)$”, Integers 7:1 (2007), #A16.