Involve: A Journal of Mathematics

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

Congruence properties of $S$-partition functions

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

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11P83: Partitions; congruences and congruential restrictions

Brandt Kronholm Ramanujan-type congruences S-partition functions


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.

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  • 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.