Work

Cubic partitions in terms of distinct partitions

Year: 2025

Type: article

Abstract: In this paper, we introduce alternative representations for the generating function of the number of cubic partitions of an integer. These new representations lead to novel formulas and provide a fresh combinatorial interpretation of cubic partitions as color partitions into distinct parts. We also obtain analogous results regarding the number of parts of size d colored identically in the cubic partitions of n and the number of cubic partitions of n that exclude parts of size d colored identically. Additionally, a new connection between an alternative sum of divisors and the 2-adic valuation is established. Furthermore, we present two open problems related to the positivity of truncated theta series within this framework.

Source: The Ramanujan Journal

DOI: 10.1007/s11139-025-01076-9

Author: Mircea Merca

Institutions: Academia Oamenilor de Știință din România, Universitatea Națională de Știință și Tehnologie Politehnica București

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,990

OpenAlex ID: W4409157534