We study the function that counts the number of partitions of with elements in , where is a set of integers. Generalizing previous work of Kronholm, we find that given a positive integer , the coefficients of the generating function of are periodic modulo , and we use this periodicity to obtain families of -partition congruences. In particular, we obtain families of congruences between partition functions and .
"Congruence properties of $S$-partition functions." Involve 4 (4) 411 - 416, 2011. https://doi.org/10.2140/involve.2011.4.411