Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Three types of the minimal excludant size of an overpartition

Thomas Y. He, C. S. Huang, H. X. Li, X. Zhang

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.

Three types of the minimal excludant size of an overpartition

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.

Paper Structure

This paper contains 8 sections, 16 theorems, 106 equations.

Table of Contents

  1. Introduction
  2. Main results of this article
  3. Results related to $mes_{r,A,a}(\pi)$
  4. Results related to $\overline{mes}_{r,A,a}(\pi)$
  5. Results related to $\widetilde{mes}_{r,A,a}(\pi)$
  6. Proofs of Theorems \ref{['gen-mes']}, \ref{['gen-sigma-mes']}, \ref{['gen-Nmes']} and \ref{['gen-Omes']}
  7. Proofs of Theorems \ref{['gen-overmes']}, \ref{['gen-sigma-overmes']} and \ref{['gen-overNmes']}
  8. Proofs of Theorems \ref{['gen-tildemes']}, \ref{['gen-sigma-tildemes']}, \ref{['gen-tildeNmes']} and \ref{['gen-tildeOmes']}

Key Result

Theorem 2.1

For $r\geq 1$,

Theorems & Definitions (16)

  • Theorem 2.1
  • Theorem 2.2
  • Theorem 2.3
  • Corollary 2.4
  • Theorem 2.5
  • Corollary 2.6
  • Theorem 2.7
  • Theorem 2.8
  • Theorem 2.9
  • Corollary 2.10
  • ...and 6 more