A note on congruences for generalized cubic partitions modulo primes

Abstract

Recently, Amdeberhan, Sellers, and Singh introduced the notion of a generalized cubic partition function $a_c(n)$ and proved two isolated congruences via modular forms, namely, $a_3(7n+4)\equiv 0(\mathrm{mod}7)$ and $a_5(11n+10)\equiv 0(\mathrm{mod}11)$. In this paper, we provide another proof of these congruences by using classical $q$-series manipulations. We also give infinite families of congruences for $a_c(n)$ for primes $p\not\equiv 1(\mathrm{mod}8)$.

arXiv comment4 pages