P. Rowley

activity

20092022

collaborators

11 papers

math.GR2022

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…

math.AT2021

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…

math.GR2021

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 $A$ , $B$ and $D$ families of Coxeter groups and certain t…

math.GR2021

Subtilings of Elnitsky Tilings for Finite Irreducible Coxeter Groups

Robert Nicolaides, Peter Rowley

Two new Elnitsky tilings for Coxeter groups of type $B$ are displayed as certain subtilings. Additionally, a new tiling for the non-crystallographic Coxeter group of type…

math.GR2021

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 $t$ is the transpose inverse automorphism of $\SL_3(q)$,…

math.GR2021

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…

math.GR2015

Maximal length elements of excess zero in finite Coxeter groups

Sarah B. Hart, Peter J. Rowley

The excess of an element $w$ of a finite Coxeter group $W$ is the minimal value of $l (x) + l (y) - l (w)$ , where $x$ , $y$ are elements of $W$ such that $x^{2} = y^{2} = 1$ and $w = x y$ .…

math.GR2014

On Excess in Finite Coxeter Groups

Sarah B. Hart, Peter J. Rowley

For a finite Coxeter group $W$ and $w$ an element of $W$ the `excess' of $w$ is defined to be $e (w) = min {ℓ (x) + ℓ (y) - ℓ (w) ∣ w = x y, x^{2} = y^{2} = 1}$ where $\el…

math.GR2014

Zero Excess and Minimal Length in Finite Coxeter Groups

Sarah B. Hart, Peter J. Rowley

Let $W$ be the set of strongly real elements of $W$ , a Coxeter group. Then for $w \in W$ , $e (w)$ , the excess of $w$ , is defined by $e(w) = \min\{\ell(x) + \ell(…

math.CO2014

Involution Statistics in Finite Coxeter Groups

Sarah B. Hart, Peter J. Rowley

Let $W$ be a finite Coxeter group and $X$ a subset of $W$ . The length polynomial $L_{W, X} (t)$ is defined by $L_{W, X} (t) = \sum_{x \in X} t^{ℓ (x)}$ , where $ℓ$ is the length fu…

math.GR2009

A 3-local characterization of Co_2

Chris Parker, Peter Rowley

Conway's second largest simple group, $\Co_2$, is characterized by the centralizer of an element of order 3 and certain fusion data.