Congruence properties ofS-partition functions
Andrew Gruet, Linzhi Wang, Katherine Yu, Jiangang Zeng · Involve a Journal of Mathematics · 2011
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).MSC2010: 11P83.