On the size of kakeya sets in finite fields
Web22 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 ... WebIn a recent breakthrough, Dvir showed that every Kakeya set in Fn must have cardinality at least cn F n, where cn≈1∕n!. We improve this lower bound to βn F ... 2008 An improved lower bound on the size of Kakeya sets over finite fields. Shubhangi Saraf, Madhu Sudan. Anal. PDE 1(3): 375-379 (2008). DOI: 10.2140/apde ...
On the size of kakeya sets in finite fields
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Web24 de ago. de 2024 · Let \mathbb {F} be a finite field consisting of q elements and let n \ge 1 be an integer. In this paper, we study the size of local Kakeya sets with respect to … WebWe study subsets of the n -dimensional vector space over the finite field F q, for odd q, which contain either a sphere for each radius or a sphere for each first coordinate of the center. We call such sets radii spherical Kakeya sets and center spherical Kakeya sets, respectively. For n ≥ 4 we prove a general lower bound on the size of any ...
WebDive into the research topics of 'On the size of kakeya sets in finite fields'. Together they form a unique fingerprint. Kakeya set Mathematics 100%. Galois field Mathematics …
WebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS ZEEV DVIR Abstract. A Kakeya set is a subset of Fn, where Fis 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 ¢ qn, where Cn depends only on n. This answers a question of Wolff [Wol99]. 1. Introduction 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 …
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 ...
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; … how many new yorkers are thereWeb16 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) … how many new zealanders fought in gallipoliWeb18 de set. de 2008 · We give improved lower bounds on the size of Kakeya and Nikodym sets over $\mathbb{F}_q^3$. We also propose a natural conjecture on the minimum … how big is a billion compared to a millionWeb10 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 … how big is a binderWeb1 de set. de 2024 · We give improved lower bounds on the size of Kakeya and Nikodym sets over $\mathbb{F}_q^3$. We also propose a natural conjecture on the minimum number of points in the union of a not-too-flat set ... how big is a blackWebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS - Read online for free. Abstract. A Kakeya set is a subset of F n, where F is a finite field of q elements, that contain a line in every direction. In this paper, we show that the size of every Kakeya set is at least Cn · q n, where Cn depends only on n. This answers a question of Wolff [Wol99]. how big is a bisonWebSaraf and M. Sudan , An improved lower bound on the size of Kakeya sets over finite fields, Anal. PDE, 1 ( 2008), pp. 375 -- 379 . Crossref ISI Google Scholar. 15. A. Warren and A. Winterhof , Conical Kakeya and Nikodym sets in finite fields, Finite Fields Appl., 59 ( 2024), pp. 185 -- 198 . Crossref ISI Google Scholar. 16. T. how many new zealanders live in usa