49 citations · 210 across the 23 of their papers we have counts for
4 papers · 1 filter
C*-algebras of self-similar actions of groupoids on higher-rank graphs and their equilibrium states
Zahra Afsar, Nathan Brownlowe, Jacqui Ramagge +1
We introduce the notion of a self-similar action of a groupoid on a finite higher-rank graph. To these actions we associate a compactly aligned product system of Hilbert bimodu…
Classification of tiling -algebras
Luke J. Ito, Michael F. Whittaker, Joachim Zacharias
We prove that Kellendonk's -algebra of an aperiodic and repetitive tiling with finite local complexity is classifiable by the Elliott invariant. Our result follows from showin…
An aperiodic tile with edge-to-edge orientational matching rules
James J. Walton, Michael F. Whittaker
We present a single, connected tile which can tile the plane but only non-periodically. The tile is hexagonal with edge markings, which impose simple rules as to how adjacent tiles…
An aperiodic monotile that forces nonperiodicity through dendrites
Michael Mampusti, Michael F. Whittaker
We introduce a new type of aperiodic hexagonal monotile; a prototile that admits infinitely many tilings of the plane, but any such tiling lacks any translational symmetry. Adding…