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On Minimal Besicovitch Arrangements in \({\mathbb {F}_q}^2\): Statistical Properties and Combinatorial Implications

  • Stéphane Blondeau Da SilvaEmail author
Original Paper
  • 16 Downloads

Abstract

In this paper, we focus on planar minimal Besicovitch arrangements to highlight some of their properties. An appropriate probability space enables us to find again in an elegant way some straightforward equalities associated with these arrangements. Resulting inequalities are also brought out. A connection with arrangements of lines in \(\mathbb {R}^2\) is eventually made, where possible.

Keywords

Besicovitch arrangements Finite field Kakeya problem 

Mathematics Subject Classification

11T99 51D20 05B05 

Notes

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Copyright information

© Iranian Mathematical Society 2019

Authors and Affiliations

  1. 1.XLIM-Mathis, UMR n°7252 CNRS-Université de LimogesLimogesFrance

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