4 papers
Computing Joins in the Weak Order of Type B Coxeter Groups: an Algorithmic Approach
Riccardo Biagioli, Lorenzo Perrone
We present an algorithm for computing the join of two elements in the weak order of the Coxeter group of type B. This extends Markowsky's algorithm for computing joins of standard…
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…
Star and weak star irreducible fully commutative elements in Coxeter groups of affine types and
Riccardo Biagioli, Luca Costantini, Elisa Sasso
The star operation, originally introduced by Kazhdan and Lusztig, was later specialized by Ernst to the so-called weak star reduction on the set of fully commutative elements of a…
Diagram Calculus for the Affine Temperley--Lieb Algebra of Type
Riccardo Biagioli, Giuliana Fatabbi, Elisa Sasso
Let (W,S) be a Coxeter system of affine type D, and let TL(W) the corresponding generalized Temperley-Lieb algebra. In this extended abstract we define an infinite dimensional asso…