Overpartitions and Kaur, Rana, and Eyyunni's mex sequences

TL;DR

This paper establishes a combinatorial bijection linking partitions with specific mex sequences to overpartitions, providing new proofs for existing results and deepening understanding of partition-related structures.

Contribution

It introduces a bijection between partitions with certain mex sequences and overpartitions, enabling combinatorial proofs of previous analytic results.

Findings

Bijection between specific partitions and overpartitions

Combinatorial proofs of Kaur, Rana, and Eyyunni's results

Enhanced understanding of mex sequences in partition theory

Abstract

Kaur, Rana, and Eyyunni recently defined the mex sequence of a partition and established, by analytic methods, connections to two disparate types of partition-related objects. We make a bijection between partitions with certain mex sequences and a uniform family of overpartitions which allows us to provide combinatorial proofs of their results, as they requested.