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## A finite version of the Kakeya problem

Autor
Ball, S.; Blokhuis, A.; Domenzain, D.
Tipus d'activitat
Article en revista
Revista
The australasian journal of combinatorics
Data de publicació
2016-06-02
Volum
65
Número
3
Pàgina inicial
251
Pàgina final
260
Repositori
http://hdl.handle.net/2117/108967
Resum
Let $L$ be a set of lines of an affine space over a field and let $S$ be a set of points with the property that every line of $L$ is incident with at least $N$ points of $S$. Let $D$ be the set of directions of the lines of $L$ considered as points of the projective space at infinity. We give a geometric construction of a set of lines $L$, where $D$ contains an $N^{n-1}$ grid and where $S$ has size $2(\frac{1}{2}N)^n$ plus smaller order terms, given a starting configuration in the plane. We prov...
Citació
Ball, S., Blokhuis, A., Domenzain, D. A finite version of the Kakeya problem. "The australasian journal of combinatorics", 2 Juny 2016, vol. 65, núm. 3, p. 251-260.
Paraules clau
Kakeya problem
Grup de recerca
GAPCOMB - Geometric, Algebraic and Probabilistic Combinatorics