Substitution Delone sets (Q1404498)

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.