Combinatorial proof of a result on generalized overcubic partitions and related conjectures

2025/12/04 by Suparno Ghoshal, Ghoshal, Suparno, Arijit Jana +1
Mathematics · Physics and Astronomy · #05A15 #05A17 #11P83 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2512.04775

openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28

Abstract

Extending Sellers' result, Das et al. recently proved some congruence results for generalized overcubic partitions using theta functions and posed some related conjectures. In this paper, we provide a combinatorial proof of a result in modulo 4 of Das et al. and confirm some of their conjectures.

Citations

• Arithmetic Properties of Generalized Cubic and Overcubic Partitions
• Two identities involving the cubic partition function

Related

• Arithmetic Properties of Generalized Cubic and Overcubic Partitions
• Proofs of two conjectures on congruences of overcubic partition triples
• Further Arithmetic Properties of Overcubic Partition Triples
• Some new congruences for generalized overcubic partition function
• Arithmetic properties of cubic and overcubic partition pairs