Work

A Combinatorial Proof of an Identity of Malik and Sarma on Overpartitions with Repeated Smallest Non-Overlined Part

Year: 2026

Type: preprint

Abstract: Motivated by the work of Andrews and El Bachraoui on partitions with repeated smallest parts, Malik and Sarma recently extended this concept to overpartitions. Using generating functions and $q$-series techniques, they established several results, including four identities, and posed the problem of finding combinatorial proofs for these identities. Recently, Baruah, Li, and Mohanta provided combinatorial proofs for three of these identities. In this paper, we present a combinatorial proof of the remaining identity.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.37966

Authors: Ghoshal, Suparno, Jana, Arijit

Institutions: National Institute Of Technology Silchar, University of Petroleum and Energy Studies

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214926668

Cites: 4

Cited by:

Related to: 10