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Substitution Delone sets. (English) Zbl 1037.52017
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.

52C23 Quasicrystals and aperiodic tilings in discrete geometry
52C22 Tilings in \(n\) dimensions (aspects of discrete geometry)
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