Computing modular coincidences

Abstract

Computing modular coincidences can show whether a given substitution system, which is supported on a point lattice in R^d, consists of model sets or not. We prove the computatibility of this problem and determine an upper bound for the number of iterations needed. The main tool is a simple algorithm for computing modular coincidences, which is essentially a generalization of Dekking coincidence to more than one dimension, and the proof of equivalence of this generalized Dekking coincidence and modular coincidence. As a consequence, we also obtain some conditions for the existence of modular coincidences. In a separate section, and throughout the article, a number of examples are given.

24 pages, 11 figures

References in corpus (3)

• Pure Point Dynamical and Diffraction Spectra
• Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces
• A Homeomorphism Invariant for Substitution Tiling Spaces

Cited by in corpus (8)

• Spectral and topological properties of a family of generalised Thue-Morse sequences
• Substitution Delone Sets with Pure Point Spectrum are Inter Model Sets
• Dynamical properties of almost repetitive Delone sets
• Squirals and beyond: Substitution tilings with singular continuous spectrum
• Hexagonal inflation tilings and planar monotiles
• Examples of substitution systems and their factors
• Algorithm for determining pure pointedness of self-affine tilings
• On the interplay between Babai and Cerny's conjectures