Three types of the minimal excludant size of an overpartition

TL;DR

This paper explores the concept of minimal excludant sizes in overpartitions, defining three new types related to the smallest missing parts, extending classical partition theory.

Contribution

It introduces three novel types of overpartition minimal excludants, expanding the understanding of overpartition structures in combinatorics.

Findings

Defined three types of overpartition minimal excludants

Extended classical partition concepts to overpartitions

Provided new combinatorial insights into overpartition structures

Abstract

Recently, Andrews and Newman studied the minimal excludant of a partition, which is defined as the smallest positive integer that is not a part of a partition. In this article, we consider the minimal excludant size of an overpartition, which is an overpartition analogue of the minimal excludant of a partition. We define three types of overpartition related to the minimal excludant size.