Intersections of sets of distances

2014/10/15 by Mauro Di Nasso, Di Nasso, Mauro
Mathematics · #05B10 #11B05 #11B37 #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematics and Applications #Point processes and geometric inequalities

paper · pdf · doi:10.48550/arxiv.1410.3973

openalex publication_date 2014/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We isolate conditions on the relative size of sets of natural numbers A,B that guarantee a nonempty intersection Δ(A)∩Δ(B)≠∅ of the corresponding sets of distances. Such conditions apply to a large class of zero density sets. We also show that a variant of Khintchine's Recurrence Theorem holds for all infinite sets A=\a₁

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