A new Garside structure for braid groups of type $(e,e,r)$

TL;DR

This paper introduces a novel Garside structure for the braid groups of type (e,e,r), providing a new presentation and diagram, and analyzing its combinatorics to classify it as post-classical.

Contribution

It presents a new monoid presentation for complex reflection groups of type (e,e,r) that yields a Garside structure, advancing understanding of their algebraic properties.

Findings

New presentation for (e,e,r) braid groups

Diagrammatic representation of the presentation

Identification of the Garside structure as post-classical

Abstract

We describe a new presentation for the complex reflection groups of type $(e,e,r)$ and their braid groups. A diagram for this presentation is proposed. The presentation is a monoid presentation which is shown to give rise to a Garside structure. A detailed study of the combinatorics of this structure leads us to describe it as post-classical.