2024/04/09 by Tewodros Amdeberhan, Ajit Singh, Amdeberhan, Tewodros +1
Mathematics · #Advanced Mathematical Identities #Mathematical and Theoretical Analysis #Functional Equations Stability Results
paper · pdf · doi:10.48550/arxiv.2404.06473
A cubic partition consists of partition pairs (λ,μ) such that \vertλ\vert+\vertμ\vert=n where μ involves only even integers but no restriction is placed on λ. 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.