Climbing elements in finite coxeter groups
Thomas Brady, Aisling Kenny, And Colum Watt
TL;DR
This paper introduces the concept of climbing elements in finite real reflection groups, characterizes them based on a total order from bipartite Coxeter elements, and explores their properties.
Contribution
It defines climbing elements in finite Coxeter groups and characterizes them using a specific total order derived from bipartite Coxeter elements.
Findings
Climbing elements are characterized in finite Coxeter groups.
A total order from bipartite Coxeter elements is used for the characterization.
The properties of these elements are systematically analyzed.
Abstract
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.
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