3 citations · 3 across the 3 of their papers we have counts for
6 papers
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…
Continuously many bounded displacement non-equivalences in substitution tiling spaces
Yaar Solomon
We consider substitution tilings in R^d that give rise to point sets that are not bounded displacement (BD) equivalent to a lattice and study the cardinality of BD(X), the set of d…
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…
On Visibility Problems with an Infinite Discrete, set of Obstacles
Michael Boshernitzan, Yaar Solomon
This paper studies visibility problems in Euclidean spaces where the obstacles are the points of infinite discrete sets . A point $x\in\mathb…
Substitution Tilings and Separated Nets with Similarities to the Integer Lattice
Yaar Solomon
We show that any primitive substitution tiling of the plane creates a separated net which is biLipschitz to the integer lattice. Then we show that if H is a primitive Pisot substit…
The net created from the Penrose tiling is biLipschitz to the integer lattice
Y. Solomon
A separated net is a set of points which is relatively dense and uniformly discrete (another name for a Delone set). We are dealing with tilings and separated nets in Euclidean spa…