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 fieldsArticle

Authors: Le Anh Vinh 1

  • 1 Department of Mathematics [Cambridge]

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.

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

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