(1) Department of Mathematics [Cambridge]
On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields
(1) Department of Mathematics [Cambridge]
English
We show that if the cardinality of a subset of the $(2k-1)$-dimensional vector space over a finite field with $q$ elements is $\gg q^{2k-1-\frac{1}{ 2k}}$, then it contains a positive proportional of all $k$-simplexes up to congruence.
French
Nous montrons que si la cardinalité d'un sous-ensemble de l'espace vectoriel à $(2k-1)$ dimensions sur un corps fini à $q$ éléments est $\gg q^{2k-1-\frac{1}{ 2k}}$, alors il contient une proportion non-nulle de tous les $k$-simplexes de congruence.
- [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO]
- [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM]
- distance problem
- finite Euclidean graphs
- finite non-Euclidean graphs
- spectral graphs
Source: OpenCitations
On a Furstenberg-Katznelson-Weiss Type Theorem over Finite Fields
Annals of Combinatorics
Authors : Le Anh Vinh 
Journal reference : Volume 15, 2011, pp. 541-547
DOI : 10.1007/s00026-011-0107-4
