Congruences and recursions for the cubic partition

TL;DR

This paper introduces new congruences modulo 11 for the cubic partition function, offers an elementary proof of a known congruence, and establishes a recursion for the function, broadening understanding of its properties.

Contribution

It presents two new congruences for cubic partitions, an elementary proof of an existing congruence, and a recursion formula for the cubic partition function.

Findings

Two new congruences modulo 11 for p_2(n)

Elementary proof of Chan's congruence

A recursion for p_2(n)

Abstract

Let $p_2(n)$ denote the number of cubic partitions. In this paper, we shall present two new congruences modulo $11$ for $p_2(n)$. We also provide an elementary alternative proof of a congruence established by Chan. Furthermore, we will establish a recursion for $p_2(n)$, which is a special case of a broader class of recursions.