R. Scott

activity

19992018

collaborators

10 papers

math.GR2018

Growth series of CAT(0) cubical complexes

Boris Okun, Richard Scott

Let $X$ be a CAT(0) cubical complex. The growth series of $X$ at $x$ is $G_{x} (t) = \sum_{y \in V er t (X)} t^{d (x, y)}$ , where $d (x, y)$ denotes $ℓ_{1}$ -distance between $x$ and $y$ .…

math.GR2013

Eulerian cube complexes and reciprocity

Richard Scott

Let $G$ be the fundamental group of a compact nonpositively curved cube complex $Y$ . With respect to a basepoint $x$ , one obtains an integer-valued length function on $G$ by counti…

math.RT2012

Kazhdan-Lusztig cells in planar hyperbolic Coxeter groups and automata

Mikhail Belolipetsky, Paul Gunnells, Richard Scott

Let C be a one- or two-sided Kazhdan--Lusztig cell in a Coxeter group (W,S), and let Reduced(C) denote the set of reduced expressions of all w in C, regarded as a language over the…

math.GR2012

The Atiyah conjecture for the Hecke algebra of the infinite dihedral group

Boris Okun, Richard Scott

We prove a generalized version of the Strong Atiyah Conjecture for the infinite dihedral group W, replacing the group von Neumann algebra NW with the Hecke-von Neumann algebra N_qW…

math.GR2011

On groups with Cayley graph isomorphic to a cube

Colin Hagemeyer, Richard Scott

We say that a group G is a cube group if it is generated by a set S of involutions such that the corresponding Cayley graph Cay(G,S) is isomorphic to a cube. Equivalently, G is a c…

math.GR2008

Reciprocity and rationality for the greedy normal form of a Coxeter group

Richard Scott

We show that the characteristic series for the greedy normal form of a Coxeter group is always a rational series, and prove a reciprocity formula for this series when the group is…