Congruence properties of S-partition functions

Gruet, Andrew; Wang, Linzhi; Yu, Katherine; Zeng, Jiangang

doi:10.2140/involve.2011.4.411

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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

DOI: 10.2140/involve.2011.4.411

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 $p (S_{1}; n)$ and $p (S_{2}; n)$ .

Keywords

Brandt Kronholm, Ramanujan-type congruences, S-partition functions

Mathematical Subject Classification 2010

Primary: 11P83

Milestones

Received: 28 April 2011

Accepted: 17 June 2011

Published: 21 March 2012

Communicated by Ken Ono

Authors

Andrew Gruet
PO Box 2054 Acton, MA 01720 United States

Linzhi Wang
No. 6 Building 14 Fuhehuayuan, Shuliang County Chihingdu, Sichuan China

Katherine Yu
51 Clearfield Dr. San Francisco, CA 94132 United States

Jiangang Zeng
1503 North Decatur Rd No. 4 Atlanta 30327 United States

Vol. 4, No. 4, 2011