New congruences for 4,6-regular partitions modulo primes

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 $m\ge 2$ and $m\ge 5$, 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 $3$.

arXiv comment13 pages. v2: Append results for b_4(n) modulo 2, b_6(n) modulo 5. v3: We find two explicit infinite families of b_4(n) modulo 3. See Theorem 1.2