New congruences for 4,6-regular partitions modulo primes

TL;DR

This paper establishes infinite families of Ramanujan-type congruences for 4- and 6-regular partition functions modulo various primes, including explicit families for modulus 3.

Contribution

It introduces new infinite families of congruences for 4- and 6-regular partitions, expanding the known results in partition congruences.

Findings

Existence of infinitely many Ramanujan-type congruences for b_4(n) and b_6(n)

New explicit examples of congruences for b_4(n) and b_6(n)

Two infinite families of congruences for b_4(n) modulo 3

Abstract

The main result of the paper is the existence of an infinitely many families of Ramanujan-type congruences for $b_4(n)$ and $b_6(n)$ modulo primes $m \geq 2$ and $m \geq 5$, respectively. We provide new examples of congruences for $b_4(n)$ and $b_6(n)$. Moreover, we find two infinite explicit infinite families of congruences for $b_4(n)$ modulo $3$.