Combinatorics and topology of the Robinson tiling

TL;DR

This paper investigates the space of Robinson tilings, establishing a unique minimal subshift, describing it via substitution, and computing its cohomology, demonstrating it as a model set.

Contribution

It introduces a substitution-based description of the Robinson tiling space and computes its cohomology, revealing its structure as a model set.

Findings

Unique minimal subshift identified

Cohomology groups computed

Robinson tiling space shown to be a model set

Abstract

We study the space of all tilings which can be obtained using the Robinson tiles (this is a two-dimensional subshift of finite type). We prove that it has a unique minimal subshift, and describe it by means of a substitution. This description allows to compute its cohomology groups, and prove that it is a model set.