Separable overpartition classes and excludant sizes of an overpartition

Y. H. Chen; Y. Q. Chen; Thomas Y. He; H. X. Huang; X. Zhang

paper

Separable overpartition classes and excludant sizes of an overpartition

arXiv:2501.12864

Abstract

An overpartition is a partition such that the first occurrence (equivalently, the last occurrence) of a number may be overlined. In this article, we investigate three contents of overpartitions. We first consider the $r$ -chain minimal and maximal excludant sizes of an overpartition. Then, we study the second minimal excludant and mex sequence of an overpartition. Finally, we introduce $L_{k}$ -overpartitions and $F_{k}$ -overpartitions, which are separable overpartition classes.