Some results on the cubic partition

TL;DR

This paper investigates congruences and inequalities related to the cubic partition function, utilizing Kruyswijk's method to derive new mathematical results and bounds.

Contribution

It introduces a novel application of Kruyswijk's method to cubic partitions, providing new congruences and bounds not previously established.

Findings

Derived new congruences for the cubic partition function

Established inequalities and upper bounds for the cubic partition numbers

Extended classical partition function techniques to cubic partitions

Abstract

In this paper we explore Kruyswijk's method and show how to obtain congruences for cubic partition. That apart we also examine inequalities for a(n) and provide upper bound for it in the fashion of the classic partition function p(n).