S. Hart

activity

20142019

most citedGroups whose locally maximal product-free sets are complete

3 citations · 5 across the 9 of their papers we have counts for

collaborators

12 papers

math.HO2019★ 2 cited

Ahab's Arithmetic; or, the mathematics of Moby-Dick

Sarah Hart

Herman Melville's novel Moby-Dick contains a surprising number of mathematical allusions. In this article we explore some of these, as well as discussing the questions that natural…

math.GR2018

A Note on Commuting Involution Graphs in Affine Coxeter Groups

Sarah Hart, Amal Sbeiti Clarke

Commuting involution graphs have been studied for finite Coxeter groups and for affine groups of classical type. The purpose of this short note is to establish some general results…

math.GR2018

Commuting Involution Graphs in Classical Affine Weyl Groups

Sarah Hart, Amal Sbeiti Clarke

In this paper we investigate commuting involution graphs in classical affine Weyl groups. Let $W$ be a classical Weyl group of rank $n$ , with $W ~$ its corresponding affine We…

math.GR2017

How many elements of a Coxeter group have a unique reduced expression?

Sarah Hart

Let $(W, R)$ be an arbitrary Coxeter system. We determine the number of elements of $W$ that have a unique reduced expression.

math.CO2016★ 3 cited

Groups whose locally maximal product-free sets are complete

Chimere S. Anabanti, Grahame Erskine, Sarah B. Hart

Let $G$ be a finite group and $S$ a subset of $G$ . Then $S$ is product-free if $S \cap S S = \emptyset$ , and complete if $G^{*} \subseteq S \cup S S$ . A product-free set is locall…

math.GR2015

A note on filled groups

Sarah Hart, Chimere Anabanti

Let $G$ be a finite group and $S$ a subset of $G$ . Then $S$ is {\em product-free} if $S \cap S S = \emptyset$ , and $S$ {\em fills} $G$ if $G^{*} \subseteq S \cup S S$ . A product-f…

math.GR2015

On a conjecture of Street and Whitehead on locally maximal product-free sets

Chimere S. Anabanti, Sarah B. Hart

Let $S$ be a non-empty subset of a group $G$ . We say $S$ is product-free if $S \cap S S = \emptyset$ , and $S$ is locally maximal if whenever $T$ is product-free and $S \subseteq T$ , t…

math.GR2015

Locally Maximal Product-free Sets of Size 3

Chimere Stanley Anabanti, Sarah Hart

Let $G$ be a group, and $S$ a non-empty subset of $G$ . Then $S$ is \emph{product-free} if $ab \in / S$ for all $a, b \in S$ . We say $S$ is \emph{locally maximal product-free} if $S…

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…