Lagarias, Jeffrey C.; Wang, Yang Substitution Delone sets. (English) Zbl 1037.52017 Discrete Comput. Geom. 29, No. 2, 175-209 (2003). This fundamental article presents a theory about substitution Delone set families, i.e. families of Delone sets \((X_1, \dots, X_n)\) which satisfy an inflation functional equation. The authors study solutions to the inflation functional equation that are discrete and including solutions that do not correspond to tilings. They develop a structure theory, and these results are proved for general inflation functional equations, without primitivity restriction. They also study multiset solutions which correspond more closely to tilings. Reviewer: Laurent Vuillon (Le Bourget du Lac) Cited in 1 ReviewCited in 23 Documents MSC: 52C23 Quasicrystals and aperiodic tilings in discrete geometry 52C22 Tilings in \(n\) dimensions (aspects of discrete geometry) Keywords:Delone sets; self-replicating multi-tilings; inflation functional equation PDFBibTeX XMLCite \textit{J. C. Lagarias} and \textit{Y. Wang}, Discrete Comput. Geom. 29, No. 2, 175--209 (2003; Zbl 1037.52017) Full Text: DOI arXiv