Ramanujan-type congruences for partition k-tuples with 5-cores

Abstract

We prove several Ramanujan-type congruences modulo powers of 5 for partition k-tuples with 5-cores, for k=2,3,4. We also prove some new infinite families of congruences modulo powers of primes for k-tuples with p-cores, where p is a prime. © The Indian National Science Academy 2024.