Separable overpartition classes and excludant sizes of an overpartition
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 Lk-overpartitions and Fk-overpartitions, which are separable overpartition classes.
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