arXiv subjects

Charles Holton

Publications and source records attributed to Charles Holton.

3 recordsLinked to original sources

arXiv2018

Uniqueness and Symmetry in Problems of Optimally Dense Packings

We analyze the general problem of determining optimally dense packings, in a Euclidean or hyperbolic space, of congruent copies of some fixed finite set of bodies. We are strongly guided by examples of aperiodic tilings in Euclidean space and a detailed analysis of a new family of examples in the hyperbolic plane. Our goal is to understand qualitative features of such optimum density problems, in particular the appropriate meaning of the uniqueness of solutions, and the role of symmetry in classfying optimally dense packings.

math.MG↗

arXiv2018

Conjugacies for Tiling Dynamical Systems

We consider tiling dynamical systems and topological conjugacies between them. We prove that the criterion of being finite type is invariant under topological conjugacy. For substitution tiling systems under rather general conditions, including the Penrose and pinwheel systems, we show that substitutions are invertible and that conjugacies are generalized sliding block codes.

math.DS↗

arXiv2004

The Rohlin property for shifts of finite type

We show that an automorphism of a unital AF C*-algebra with the approximate Rohlin property has the Rohlin property. This generalizes a result of Kishimoto. Using this we show that the shift automorphism on the bilateral C*-algebra associated with an aperiodic irreducible shift of finite type has the Rohlin property.

math.FA↗