3 papers
math.GR2026
Weak order on groups generated by involutions
Fabricio Dos Santos, Christophe Hohlweg, Aleksandr Trufanov
In this article, we propose to initiate the general study of involution systems. An {\em involution system}, that is, a group generated by a set of involutions , is naturall…
math.CO2026
A conjecture on descents, inversions and the weak order
Christophe Hohlweg, Viviane Pons
In this article, we discuss the notion of partition of elements in an arbitrary Coxeter system : a partition of an element is a subset such that…
math.GR2026
On generating functions and automata associated to reflections in Coxeter systems
Riccardo Biagioli, Christophe Hohlweg, Elisa Sasso
In this article, we study two combinatorial problems concerning the set of reflections of a Coxeter system. The first problem asks whether the language of palindromic reduced words…