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On the size of kakeya sets in finite fields

Web10 de dez. de 2009 · Using the polynomial method of Dvir [On the size of Kakeya sets in finite fields. Preprint], we establish optimal estimates for Kakeya sets and Kakeya maximal functions associated to algebraic varieties W over finite fields F. WebOn the size of Kakeya sets in finite fields Zeev Dvir ∗ Abstract A Kakeya set is a subset of Fn, where F is a finite field of q elements, that contains a line in every direction. In this …

On the size of Kakeya sets in finite fields - Semantic Scholar

Web30 de jul. de 2024 · Sharp density bounds on the finite field Kakeya problem @inproceedings{Bukh2024SharpDB, title= ... Improved lower bounds on the size of … Web15 de ago. de 2024 · Till recently, the best known lower bound on the size of Kakeya sets was of the form q αn for some α < 1. In a recent breakthrough Dvir [1] showed that every Kakeya set must have cardinality at ... cure dream my little pony https://mertonhouse.net

ON THE SIZE OF KAKEYA SETS IN FINITE FIELDS Introduction

WebDefinition 1 (Kakeya Set) A set K ⊆ F n is said to be a Kakeya set in F n, if for every b ∈ F n, there exists a point a ∈ F n such that for every t ∈ F, the point a + t · b ∈ K. In other words, K contains a “line” in every “direction”. The question of establishing lower bounds on the size of Kakeya sets was posed in Wolff [7]. Web4 de jun. de 2024 · A Kakeya set contains a line in each direction. Dvir proved a lower bound on the size of any Kakeya set in a finite field using the polynomial method. We prove analogues of Dvir's result for non-degenerate conics, that is, parabolae and hyperbolae (but not ellipses which do not have a direction). We also study so-called … Webobservation that a product of Kakeya sets is also a Kakeya set. Corollary 1.1. For every integer n and every ǫ > 0 there exists a constant Cn,ǫ, de-pending only on n and ǫ such that any Kakeya set K ⊂ Fn satisfies K ≥ Cn,ǫ ·qn−ǫ, Proof. Observe that, for every integer r > 0, the Cartesian product Kr ⊂ Fn·r is also a Kakeya set. easyfatt cloud login

[0803.2336] On the size of Kakeya sets in finite fields - arXiv.org

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On the size of kakeya sets in finite fields

Improved lower bound on the size of Kakeya sets over finite fields

WebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS ZEEVDVIR 1.Introduction Let𝔽denoteafinitefieldof𝑞elements.AKakeya set(alsocalledaBesicovitch … Web22 de fev. de 2013 · On the size of Kakeya sets in finite vector spaces. For a finite field GF (q) a Kakeya set K is a subset of GF (q)^n that contains a line in every direction. This …

On the size of kakeya sets in finite fields

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Web18 de ago. de 2008 · Download a PDF of the paper titled Improved lower bound on the size of Kakeya sets over finite fields, by Shubhangi Saraf and Madhu Sudan. PDF; …

WebAbstract. A Kakeya set is a subset of n, where is a finite field of q elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least … WebA Kakeya set is a subset of F n, where F is a finite field of q elements, that contains a line in every direction. In this paper we show, for any ǫ&gt; 0, that the size of every Kakeya set is …

Web10 de dez. de 2009 · Using the polynomial method of Dvir [On the size of Kakeya sets in finite fields. Preprint], we establish optimal estimates for Kakeya sets and Kakeya … WebA Kakeya set is a subset of {F}^n , where {F} is a finite field of q elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least …

Web14 de out. de 2024 · Read article at ArXiv. Simple proofs for Furstenberg sets over finite fields, Discrete Analysis 2024:22, 16 pp. A Kakeya set in R 2 is a subset that contains a unit line segment in every direction. A well-known result of Besicovitch states that there are Kakeya sets of measure zero. This has led to numerous further results and some …

WebA Kakeya set is a subset of F n, where F is a finite field of q elements, that contains a line in every direction. In this paper we show that the size of every Kakeya set is at least Cn · q … cured resin concentrateWebWe give improved lower bounds on the size of Kakeya and Nikodym sets over $\\Bbb{F}_q^3$. We also propose a natural conjecture on the minimum number of points in the union of a not-too-flat set of lines in $\\Bbb{F}_q^3$ and show that this conjecture implies an optimal bound on the size of a Nikodym set. easy father\u0027s day giftsWeb16 de abr. de 2008 · In this paper, we study the size of local Kakeya sets with respect to subsets of Fn and obtain upper and lower bounds for the minimum size of a (local) … cured pork ham steakWeb22 de fev. de 2013 · PDF For a finite field GF(q) a Kakeya set K is a subset of GF(q)^n that contains a line in every direction. This paper derives new upper bounds on the... Find, read and cite all the research ... easy fat burning workoutWebA Kakeya set is a subset of F n, where F is a finite field of q elements, that contains a line in every direction. In this paper we show that every Kakeya set is of size at least Cn·q … easy fat bomb recipes with coconut oilWeb1 de set. de 2024 · A Kakeya set contains a line in each direction. Dvir proved a lower bound on the size of any Kakeya set in a finite field using the polynomial method. We prove analogues of Dvir's result for non-degenerate conics, that is, parabolae and hyperbolae (but not ellipses which do not have a direction). easy fast weight loss diet planWeb1 de mai. de 2007 · Bolyai Soc Math Stud 19 (2008) 205–218) provide a strong answer to the finite field analog of the classical Kakeya problem, which asks for the minimum size of a point set in an affine plane π ... easy father\u0027s day cards