7 citations · 19 across the 13 of their papers we have counts for
19 papers
Degenerating orbits of the Longest Edge Bisection process
Karim A. Adiprasito, Daniel Kalmanovich, Yaar Solomon
We study the Longest Edge Bisection (LEB) process as a dynamical system on the projective shape space of simplices. A long-standing conjecture going back to Adler and Rivara-Levin…
BiLipschitz and bounded displacement equivalence of Delone sets
Yotam Smilansky, Yaar Solomon
We survey biLipschitz (BL) and bounded displacement (BD) equivalence of Delone sets, with an emphasis on examples arising in aperiodic order. After recalling the classical results…
On the stability, complexity, and distribution of similarity classes of the longest edge bisection process for triangles
Daniel Kalmanovich, Yaar Solomon
The Longest Edge Bisection of a triangle is performed by joining the midpoint of its longest edge to the opposite vertex. Applying this procedure iteratively produces an infinite f…
Periodicity of joint co-tiles in
Tom Meyerovitch, Shrey Sanadhya, Yaar Solomon
An old theorem of Newman asserts that any tiling of by a finite set is periodic. A few years ago, Bhattacharya proved the periodic tiling conjecture in .…
A note on reduction of tiling problems
Tom Meyerovitch, Shrey Sanadhya, Yaar Solomon
We show that translational tiling problems in a quotient of can be effectively reduced or ``simulated'' by translational tiling problems in . In partic…
Discrepancy and rectifiability of almost linearly repetitive Delone sets
Yotam Smilansky, Yaar Solomon
We extend a discrepancy bound of Lagarias and Pleasants for local weight distributions on linearly repetitive Delone sets and show that a similar bound holds also for the more gene…
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…
Multiscale Substitution Tilings
Yotam Smilansky, Yaar Solomon
We introduce a new general framework for constructing tilings of Euclidean space, which we call multiscale substitution tilings. These tilings are generated by substitution schemes…
Cut-and-project quasicrystals, lattices, and dense forests
Faustin Adiceam, Yaar Solomon, Barak Weiss
Dense forests are discrete subsets of Euclidean space which are uniformly close to all sufficiently long line segments. The degree of density of a dense forest is measured by its v…
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…
On problems of Danzer and Gowers and dynamics on the space of closed subsets of
Omri Solan, Yaar Solomon, Barak Weiss
Considering the space of closed subsets of , endowed with the Chabauty-Fell topology, and the affine action of , we prove that th…
A Danzer set for Axis Parallel Boxes
David Simmons, Yaar Solomon
We present concrete constructions of discrete sets in () that intersect every aligned box of volume in , and which have optimal growth rate…
Dense forests and Danzer sets
Yaar Solomon, Barak Weiss
A set that intersects every convex set of volume is called a Danzer set. It is not known whether there are Danzer sets in with growth ra…
A Simple Condition for Bounded Displacement
Yaar Solomon
We study separated nets that correspond to substitution tilings of the Euclidean space. We give a simple condition, in terms of the eigenvalues and eigenspaces of the substitution…
Functions of Substitution Tilings as a Jacobian
Yaar Solomon
In this paper we show that the function defined by a primitive, star shaped substitu- tion tiling of the plane, can be realized as a Jacobian of a biLipschitz homeomorphism of R^2.…
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…