Bases for the Bruhat–Chevalley Order on All Finite Coxeter Groups

Bases for the Bruhat{chevalley Order on All Nite Coxeter Groups

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 ...

Gröbner-shirshov Bases for Coxeter Groups I *

A conjecture of Gröbner-Shirshov basis of any Coxeter group has proposed by L.A. Bokut and L.-S. Shiao [4]. In this paper, we give an example to show that the conjecture is not true in general. We list all possible nontrivial inclusion compositions when we deal with the general cases of the Coxeter groups. We give a Gröbner-Shirshov basis of a Coxeter group which is without nontrivial inclusion...

The Order Dimension of Bruhat Order on Infinite Coxeter Groups

We give a quadratic lower bound and a cubic upper bound on the order dimension of the Bruhat (or strong) ordering of the affine Coxeter group Ãn. We also demonstrate that the order dimension of the Bruhat order is infinite for a large class of Coxeter groups.

The Finite Antichain Property in Coxeter Groups

We prove that the weak order on an infinite Coxeter group contains infinite antichains if and only if the group is not affine.