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

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.

References in corpus (5)

• Zariski theorems and diagrams for braid groups
• Enumerative properties of generalized associahedra
• Non-crossing partitions of type (e,e,r)
• Garside structure for the braid group of G(e,e,r)
• Topology of complex reflection arrangements

Cited by in corpus (4)

• The center of pure complex braid groups
• Braid groups of imprimitive complex reflection groups
• Periodic elements in Garside groups
• Interval Garside Structures Related to the Affine Artin Groups of Type $\tilde{A}$