On the size of kakeya sets in finite fields
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 … WebSaraf 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.
On the size of kakeya sets in finite fields
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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. 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; …
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 ... Web16 de mar. de 2008 · The motivation for studying Kakeya sets over finite fields is to try to better understand the more complicated questions regarding Kakeya sets in W1. A …
Web22 de fev. de 2013 · On the Size of Kakeya Sets in Finite Vector Spaces. Electron. J. Comb. For a finite field $\mathbb {F}_q$, a Kakeya set $K$ is a subset of $\mathbb {F}_q^n$ … WebNote that if K0ˆR2 is a Kakeya set, then K:= K0 [0;1]n 2 is a Kakeya set in Rn, and moreover, if K0has measure zero, then Kalso has measure zero, so Kakeya sets, even when considered in Rn, can be of arbitrarily small measure, given Besicovitch’s result. Thus, it is natural to ask if there’s any di erence between small Kakeya sets of di ...
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. We show: …
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 … imas f3 chapter 1Web14 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 … imase night dancer lyrics romanizedWebON 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]. imase twitterWeb29 de jan. de 2011 · Abstract. For a finite vector space V and a nonnegative integer r ≤dim V, we estimate the smallest possible size of a subset of V, containing a translate of every r -dimensional subspace. In particular, we show that if K ⊆ V is the smallest subset with this property, n denotes the dimension of V, and q is the size of the underlying field ... imase night dancer的歌詞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 … ima set your house on fire lyricsWebobservation 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. imase with punpee \u0026 toby fox - pale rainWebCiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): A 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> 0, that the size of every Kakeya set is at least Cn,ǫ · q n−ǫ, where Cn,ǫ depends only on n and ǫ. This improves the previously best … list of home finance companies in india