Intersections of shifted sets
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...
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| Main Author | |
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| Format | Journal Article |
| Language | English |
| Published |
28.11.2014
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| Subjects | |
| Online Access | Get full text |
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| 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. |
|---|---|
| AbstractList | 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. |
| Author | Di Nasso, Mauro |
| Author_xml | – sequence: 1 givenname: Mauro surname: Di Nasso fullname: Di Nasso, Mauro |
| BackLink | https://doi.org/10.48550/arXiv.1411.7832$$DView paper in arXiv |
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| Snippet | 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... |
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| Title | Intersections of shifted sets |
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