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...
Saved in:
Main Author | |
---|---|
Format | Journal Article |
Language | English |
Published |
28.11.2014
|
Subjects | |
Online Access | Get full text |
Cover
Loading…
Summary: | 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: | 10.48550/arxiv.1411.7832 |