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

2025/05/28 by Brian Hopkins, Hopkins, Brian, James A. Sellers +1
Computer Science · Mathematics · #05A17 (primary) 11P81 (secondary) #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2505.22588

openalex publication_date 2025/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• A bijective proof of a generalization of the non-negative crank--odd mex identity
• Partitions and the Minimal Excludant

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• Mex-related partitions and relations to ordinary partition and singular overpartitions
• On new minimal excludants of overpartitions related to some q-series of Ramanujan
• Schmidt Type Partitions
• Separable overpartition classes and the r-chain excludant sizes of an overpartition