Intersections of Shifted Sets

  • Mauro Di Nasso
Keywords: Asymptotic density, Delta-sets, k-Recurrence sets

Abstract

We consider shifts of a set $A\subseteq\mathbb{N}$ by elements from another set $B\subseteq\mathbb{N}$, 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 $R_k(A)=\{x\mid |A\cap(A+x)|\ge k\}$ contains the distance sets  of arbitrarily large finite sets.
Published
2015-05-14
Article Number
P2.25