Computing modular coincidences

Details Computing modular coincidences Computing modular coincidences

2006-01-04

arxiv.org/abs/math/0601067v2

Discrete Comput. Geom. 37, No.3, 381-401 (2007)

Mathematics

Metric Geometry

24 pages, 11 figures

Scientific paper

10.1007/s00454-006-1280-9

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.

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