Work

Overpartitions in terms of 2-adic valuation

Year: 2024

Type: article

Abstract: In this paper, we consider the 2-adic valuation of integers and provide an alternative representation for the generating function of the number of overpartitions of an integer. As a consequence of this result, we obtain a new formula and a new combinatorial interpretation for the number of overpartitions of an integer. This formula implies a certain type of partitions with restrictions for which we provide two Ramanujan-type congruences and present as open problems two infinite families of linear inequalities. Connections between overpartitions and the game of m-Modular Nim with two heaps are presented in this context.

Source: Aequationes Mathematicae

DOI: 10.1007/s00010-024-01117-6

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: W4402314471