On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields

Le Anh Vinh

doi:10.46298/dmtcs.2701

Le Anh Vinh - On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields

dmtcs:2701 - Discrete Mathematics & Theoretical Computer Science, January 1, 2009, DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009) - https://doi.org/10.46298/dmtcs.2701

On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fieldsConference paper

Authors: Le Anh Vinh ¹

1 Department of Mathematics [Cambridge]

[en]
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.

[fr]
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.

https://doi.org/10.46298/dmtcs.2701

Source: HAL:hal-01185393v1

Volume: DMTCS Proceedings vol. AK, 21st International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2009)

Section: Proceedings

Published on: January 1, 2009

Imported on: January 31, 2017

Keywords: [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], [en] distance problem, finite Euclidean graphs, finite non-Euclidean graphs, spectral graphs

Le Anh Vinh - On $k$-simplexes in $(2k-1)$-dimensional vector spaces over finite fields

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