5 papers · 1 filter
Finding Bounded Simplicial Sets with Finite Homology
Preston Cranford, Peter Rowley
The central problem in computational algebraic topology is the computation of the homotopy groups of a given space, represented as a simplicial set. Algorithms have been found whic…
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…