Intersections of shifted sets

2014/11/28 by Mauro Di Nasso, Di Nasso, Mauro
Mathematics · #05B10 #11B05 #11B37 #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #math.CO #msc:05B10 #msc:11B05 #msc:11B37

paper · pdf · doi:10.48550/arxiv.1411.7832

arxiv created 2014/11/28 · openalex publication_date 2014/11/28 · arxiv updated 2014/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider shifts of a set A⊆ℕ by elements from another set B⊆ℕ, and prove intersection properties according to the relative asymptotic size of A and B. A consequence of our main theorem is the following: If A=\a_n\ is such that a_n=o(n^k/k-1), then the k-recurrence set R_k(A)=\x| |A∩(A+x)|≥ k\ contains the distance sets of arbitrarily large finite sets.

Related

• Intersections of sets of distances
• Around the Complete Intersection Theorem
• Families intersecting on an interval
• Intersection patterns and connections to distance problems
• On the maximum of the sum of the sizes of non-trivial cross-intersecting families