Corpus ID: 236772269

# Sharp density bounds on the finite field Kakeya

@inproceedings{Bukh2021SharpDB,
title={Sharp density bounds on the finite field Kakeya},
author={Boris Bukh and Ting-Wei Chao},
year={2021}
}
• Published 2021
• Mathematics
A Kakeya set in F q is a set containing a line in every direction. We show that every Kakeya set in F q has density at least 1/2, matching the construction by Dvir, Kopparty, Saraf and Sudan.

#### References

SHOWING 1-6 OF 6 REFERENCES
The Finite Field Kakeya Problem
• Mathematics
• 2008
A Besicovitch set in AG(n, q) is a set of points containing a line in every direction. The Kakeya problem is to determine the minimal size of such a set. We solve the Kakeya problem in the plane, andExpand
Improved lower bound on the size of Kakeya sets over finite fields
• Mathematics
• 2008
In a recent breakthrough, Dvir showed that every Kakeya set in $\F^n$ must be of cardinality at least $c_n |\F|^n$ where $c_n \approx 1/n!$. We improve this lower bound to $\beta^n |\F|^n$ for aExpand
Finite Field Kakeya and Nikodym Sets in Three Dimensions
• Computer Science, Mathematics
• SIAM J. Discret. Math.
• 2018
Improved lower bounds on the size of Kakeya and Nikodym sets over $\mathbb{F}_q^3$ are given and a natural conjecture on the minimum number of points in the union of a not-too-flat set of lines is proposed. Expand
On the size of Kakeya sets in finite fields
The motivation for studying Kakeya sets over finite fields is to try to better understand the more complicated questions regarding Kakeya sets in W1. A Kakeya set K C Rn is a compact set containing aExpand
Extensions to the Method of Multiplicities, with Applications to Kakeya Sets and Mergers
• Computer Science, Mathematics
• 2009 50th Annual IEEE Symposium on Foundations of Computer Science
• 2009
The "method of multiplicities" is extended to get results, of interest in combinatorics and randomness extraction, that prove, under appropriate conditions, that the interpolating polynomial vanishes {\em with high multiplicity} outside the set. Expand
A proof of the Multijoints Conjecture and Carbery's generalization
We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in anyExpand