Skew plane partitions according to the $m$th largest and $m$th smallest parts

TL;DR

This paper generalizes the study of the $m$th largest and smallest parts of partitions to skew plane partitions by introducing skew plane overpartitions, expanding the combinatorial framework.

Contribution

It introduces skew plane overpartitions and extends existing results to this new class, broadening the understanding of partition statistics.

Findings

Extended results to skew plane overpartitions

Defined new combinatorial objects called skew plane overpartitions

Generalized previous partition theorems to a broader context

Abstract

We extend recent results by G. E. Andrews and G. Simay on the $m$th largest and $m$th smallest parts of a partition to the more general context of skew plane partitions. In order to do this, we introduce new objects called skew plane overpartitions.