Congruences for partition quadruples with f-cores

Abstract

Let Ct,(n) denote the number of partition quadruples of n with t-cores for t - 3. 5. 7, 25. We establish some Ramanujan type congruences modulo 5, 7, 8 for Ct,(n). For example, n ≥ 0, we have C₅(5/r 4-4) = 0 (mod 5), C₇(7n 4-6) =0 (mod 7), C₃(16/J 4- 14) = 0 (mod 8).