Geodesic
Intersections of shifted sets
Mauro Di Nasso1
1University of Pisa, Italy
The electronic journal of combinatorics, Tome 22 (2015) no. 2
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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.
DOI : 10.37236/4861
Classification : 05B10, 11B05, 11B37
Mots-clés : asymptotic density, delta-sets, \(k\)-recurrence sets

Mauro Di Nasso  1

1 University of Pisa, Italy 
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Mauro Di Nasso. Intersections of shifted sets. The electronic journal of combinatorics, Tome 22 (2015) no. 2. doi: 10.37236/4861

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