Determining the maximum difference between the number of atoms and number of coatoms of a Bruhat interval of the symmetric group

TL;DR

This paper identifies the maximum possible difference between the count of atoms and coatoms within Bruhat intervals of the symmetric group, providing insights into their combinatorial structure.

Contribution

It precisely determines the maximum difference between atoms and coatoms in Bruhat intervals of the symmetric group, a new combinatorial result.

Findings

Maximum difference between atoms and coatoms is explicitly calculated.

The result applies to all symmetric groups $S_n$.

Provides a new understanding of Bruhat interval structures.

Abstract

We determine the largest difference between the number of atoms and number of coatoms of a Bruhat interval of $S_n$.