Integer Sequences Realized by the Subgroup Pattern of the Symmetric Group

TL;DR

This paper explores the integer sequences generated by the subgroup pattern of the symmetric group, providing insights into the structure and enumeration of subgroups within this fundamental group class.

Contribution

It introduces a collection of sequences realized specifically by the subgroup pattern of the symmetric group, expanding understanding of subgroup enumeration.

Findings

Identified specific integer sequences associated with symmetric group subgroup patterns.

Provided a detailed description of the subgroup pattern structure.

Enhanced the catalog of sequences related to finite group subgroup configurations.

Abstract

The subgroup pattern of a finite group $G$ is the table of marks of $G$ together with a list of representatives of the conjugacy classes of subgroups of $G$. In this article we describe a collection of sequences realized by the subgroup pattern of the symmetric group.