Relating Edelman-Greene insertion to the Little map

TL;DR

This paper demonstrates how the Little map factors through Edelman-Greene insertion, establishing new theoretical results and resolving conjectures related to symmetric group decompositions.

Contribution

It shows the Little map factors through Edelman-Greene insertion and resolves several conjectures, advancing understanding of combinatorial algorithms in symmetric groups.

Findings

The Little map factors through Edelman-Greene insertion.

Resolved conjectures of Lam and Little.

Established new theoretical connections between the maps.

Abstract

The Little map and the Edelman-Greene insertion algorithm, a generalization of the Robinson-Schensted correspondence, are both used for enumerating the reduced decompositions of an element of the symmetric group. We show the Little map factors through Edelman-Greene insertion and establish new results about each map as a consequence. In particular, we resolve some conjectures of Lam and Little.