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 that is shown to give rise to a Garside structure. This structure has since been used in understanding periodic elements, calculating homology and determining the centre of a pure braid group. A detailed study of the combinatorics of this structure leads us to describe it as post-classical.

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