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math.DS2026
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…
math.DS2026
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…
cs.CG2026
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…