Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function

Abstract

For any non-negative integer $n$ and non-zero integer $r$, let $p_r(n)$ denote Ramanujan's general partition function. By employing $q$-identities, we prove some new Ramanujan-type congruences modulo 5 for $p_r(n)$ for $r=-(5\lambda+1), -(5\lambda+3), -(5\lambda+4), -(25\lambda+1)$, $-(25\lambda+2)$, and any integer $\lambda$.