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

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).

Brandt Kronholm, Ramanujan-type congruences, S-partition functions
Mathematical Subject Classification 2010
Primary: 11P83
Received: 28 April 2011
Accepted: 17 June 2011
Published: 21 March 2012

Communicated by Ken Ono
Andrew Gruet
PO Box 2054
Acton, MA 01720
United States
Linzhi Wang
No. 6 Building 14
Fuhehuayuan, Shuliang County
Chihingdu, Sichuan
Katherine Yu
51 Clearfield Dr.
San Francisco, CA 94132
United States
Jiangang Zeng
1503 North Decatur Rd
No. 4
Atlanta 30327
United States