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math.MG2020
A dichotomy for bounded displacement equivalence of Delone sets
Yotam Smilansky, Yaar Solomon
We prove that in every compact space of Delone sets in which is minimal with respect to the action by translations, either all Delone sets are uniformly spread, or c…
math.MG2019
Bounded Displacement Non-Equivalence In Substitution Tilings
Dirk Frettlöh, Yotam Smilansky, Yaar Solomon
In the study of aperiodic order and mathematical models of quasicrystals, questions regarding equivalence relations on Delone sets naturally arise. This work is dedicated to the bo…