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2011 Congruence properties of $S$-partition functions
Andrew Gruet, Linzhi Wang, Katherine Yu, Jiangang Zeng
Involve 4(4): 411-416 (2011). 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(S1;n) and p(S2;n).

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Andrew Gruet. Linzhi Wang. Katherine Yu. Jiangang Zeng. "Congruence properties of $S$-partition functions." Involve 4 (4) 411 - 416, 2011. https://doi.org/10.2140/involve.2011.4.411

Information

Received: 28 April 2011; Accepted: 17 June 2011; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1279.11103
MathSciNet: MR2905237
Digital Object Identifier: 10.2140/involve.2011.4.411

Subjects:
Primary: 11P83

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

Rights: Copyright © 2011 Mathematical Sciences Publishers

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