7 papers
The Bruhat Order of a Finite Coxeter Group and Elnitsky Tilings
Robert Nicolaides, Peter Rowley
Suppose that is a finite Coxeter group and a standard parabolic subgroup of . The main result proved here is that for any for any and reduced expression of $…
The Deletion Order and Coxeter Groups
Robert Nicolaides, Peter Rowley
The deletion order of a finitely generated Coxeter group W is a total order on the elements which, as is proved, is a refinement of the Bruhat order. This order is applied in [8] t…
A Note on the Rank 5 Polytopes of M24
Veronica Kelsey, Robert Nicolaides, Peter Rowley
The maximal rank of an abstract regular polytope for M24, the Mathieu group of degree 24, is 5. There are four such polytopes of rank 5 and in this note we describe them using Curt…
Finite Coxeter Groups and Generalized Elnitsky Tilings
Robert Nicolaides, Peter Rowley
In [5], Elnitsky constructed three elegant bijections between classes of reduced words for Type , and families of Coxeter groups and certain t…
Subtilings of Elnitsky Tilings for Finite Irreducible Coxeter Groups
Robert Nicolaides, Peter Rowley
Two new Elnitsky tilings for Coxeter groups of type are displayed as certain subtilings. Additionally, a new tiling for the non-crystallographic Coxeter group of type…
Unravelled Abstract Regular Polytopes
Robert Nicolaides, Peter Rowley
This paper introduces the notion of an unravelled abstract regular polytope, and proves that $\SL_3(q) \rtimes <t>$, where is the transpose inverse automorphism of $\SL_3(q)$,…
Two Families of Unravelled Abstract Regular Polytopes in Bn
Robert Nicolaides, Peter Rowley
This paper exhibits two families of unravelled abstract regular polytopes in Coxeter groups of type Bn. For one family they have rank 4 while the other family has arbitrarily large…