Some spectral results on Kakeya sets
-
Jeremy M. Dover
and
Keith E. Mellinger
Abstract
The finite field Kakeya problem asks both the minimum size of a point set inAG(2, q)which contains a line in every direction, as well as a characterization of the examples. Blokhuis and Mazzocca [2] solved this problem, and a subsequent paper [1] addresses the stability of this solution for even order planes, i.e. the spectrum of sizes near the minimum size of a Kakeya set for which non-minimum Kakeya sets exist. In this paper we provide some computational results in small order planes to determine the full spectrum of sizes of Kakeya sets. We then address some spectrum issues on the upper end of possible sizes, providing some bounds and new constructions.We also address the question of minimality, i.e.whether a given Kakeya set contains any smaller Kakeya set.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Frontmatter
- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
- Projective normality and the generation of the ideal of an Enriques surface
- Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
- Torsion-free G*2(2)-structures with full holonomy on nilmanifolds
Articles in the same Issue
- Frontmatter
- A natural extension of the Young partition lattice
- Pencils of small degree on curves on unnodal Enriques surfaces
- Michael’s Selection Theorem in a semilinear context
- Quasi-simple Lie groups as multiplication groups of topological loops
- Some spectral results on Kakeya sets
- Projective normality and the generation of the ideal of an Enriques surface
- Topological contact dynamics I: symplectization and applications of the energy-capacity inequality
- Torsion-free G*2(2)-structures with full holonomy on nilmanifolds
