H. Gimenez

collaborators

3 papers

math.GR2026

On the Weak Right Order of a Right-Angled Coxeter System

Harrison Gimenez

Let $(W, S)$ be a Coxeter system, and let $w \in W$ . Let $[1, w] := {x \in W ∣ x \leq_{R} w}$ where $\leq_{R}$ denotes the weak right order of $(W, S)$ . The element $w$ is…

math.GR2026

Root Systems, Tits Cones and Imaginary Cones of Brink-Howlett Groupoids

Matthew Dyer, Harrison Gimenez

We extend the basic theory of the groupoids introduced by Brink and Howlett in their study of normalizers of parabolic subgroups of Coxeter groups, by studying both their abstract…

math.GR2025

Coxeter systems, left inversion sets, and higher dimensional cubes

Harrison Gimenez

Let $(W, S)$ be a Coxeter system. We investigate the equation $w (I^¦_{x}) = I^¦_{y}$ where $w, x, y \in W$ and $I^¦_{x}$ , $I^¦_{y}$ denote the left inversion sets of $x$ and $y$ . We…