Generalized cubic partitions

Abstract

A cubic partition consists of partition pairs $(\lambda ,\mu )$ such that $|\lambda |+|\mu |=n$ where $\mu$ involves only even integers but no restriction is placed on $\lambda$. This paper initiates the notion of generalized cubic partitions and will prove a number of new congruences akin to the classical Ramanujan-type. The tools emphasize three methods of proofs. The paper concludes with a conjecture on the rarity of the aforementioned Ramanujan-type congruences.

The preprint contains a wrong conjecture and the paper's content will be completely changed from the current form. Not to be replaced