Ramanujan-type Congruences for Partition $k$-Tuples with $5$-Cores

TL;DR

This paper establishes new Ramanujan-type congruences modulo powers of 5 for partition k-tuples with 5-cores, and extends these results to other primes, revealing infinite families of congruences.

Contribution

It introduces new Ramanujan-type congruences for partition k-tuples with p-cores, generalizing previous results and providing infinite families of such congruences for primes.

Findings

Ramanujan-type congruences modulo powers of 5 for k=2,3,4

New infinite families of congruences modulo powers of primes for p-cores

Extension of congruences to general primes p

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.