Presentations of Coxeter groups of type $A$, $B$, and $D$ using prefix-reversal generators

TL;DR

This paper introduces three new presentations of Coxeter groups of types A, B, and D using prefix reversals as generators, and proves their equivalence to standard presentations through Tietze transformations.

Contribution

The paper provides novel presentations of Coxeter groups of types A, B, and D using prefix-reversal generators, expanding the understanding of their algebraic structure.

Findings

New presentations of Coxeter groups A, B, and D using prefix reversals

Proof of equivalence to standard presentations via Tietze transformations

Enhanced understanding of group generators and relations

Abstract

Here we provide three new presentations of Coxeter groups type $A$, $B$, and $D$ using prefix reversals (pancake flips) as generators. We prove these presentations are of their respective groups by using Tietze transformations on the presentations to recover the well known presentations with generators that are adjacent transpositions.