Oriented distance point of view on random sets

Fuzzy sets form A meta-system-theoretic point of view

Distance Sets of Well-Distributed Planar Point Sets

We prove that a well-distributed subset of R2 can have a distance set ∆ with #(∆ ∩ [0, N ]) ≤ CN3/2− only if the distance is induced by a polygon K. Furthermore, if the above estimate holds with = 1/2, then K can have only finitely many sides.

fuzzy sets form a meta-system-theoretic point of view

On two-point configurations in subsets of pseudo-random sets

We prove a transference type result for pseudo-random subsets of Z N that is analogous to the well-known Fürstenberg-Sárközy theorem. More precisely, let k 2 be an integer and let and be real numbers satisfying + ()/(2 k+1 3) > 1. Let ✓ Z N be a set with size at least N and linear bias at most N. Then, every A ✓ with relative density |A|/|| (log log N) 1 2 log log log log log N contains a pair ...

On the Choi e of Quasi - Random Point Sets