A Construction for Difference Sets with Local Properties.
2018
We construct finite sets of real numbers that have a small difference set and strong local properties. In particular, we construct a set $A$ of $n$ real numbers such that $|A-A|=n^{\log_2 3}$ and that every subset $A'\subseteq A$ of size $k$ satisfies $|A'-A'|\ge k^{\log_2 3}$. This construction leads to the first non-trivial upper bound for the problem of distinct distances with local properties.
Keywords:
- Correction
- Cite
- Save
- Machine Reading By IdeaReader
0
References
0
Citations
NaN
KQI