Climbing elements in finite Coxeter groups

Climbing Elements in Finite Coxeter Groups

We define the notion of a climbing element in a finite real reflection group relative to a total order on the reflection set and we characterise these elements in the case where the total order arises from a bipartite Coxeter element.

Essays on Coxeter groups Coxeter elements in finite Coxeter groups

A finite Coxeter group possesses a distinguished conjugacy class of Coxeter elements. The literature about these is very large, but it seems to me that there is still room for a better motivated account than what exists. The standard references on thismaterial are [Bourbaki:1968] and [Humphreys:1990], butmy treatment follows [Steinberg:1959] and [Steinberg:1985], from which the clever parts of ...

Maximal Length Elements of Excess Zero in Finite Coxeter Groups

Braided Elements in Coxeter Groups , Ii

We continue the study of freely braided elements of simply laced Coxeter groups, which we introduced in a previous work. A known upper bound for the number of commutation classes of reduced expressions for an element of a simply laced Coxeter group is shown to be achieved only when the element is freely braided; this establishes the converse direction of a previous result. It is also shown that...

Sortable Elements in Infinite Coxeter Groups

In a series of previous papers, we studied sortable elements in finite Coxeter groups, and the related Cambrian fans. We applied sortable elements and Cambrian fans to the study of cluster algebras of finite type and the noncrossing partitions associated to Artin groups of finite type. In this paper, as the first step towards expanding these applications beyond finite type, we study sortable el...