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

Source 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.