On the size of kakeya sets in finite fields

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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 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 …

The Spherical Kakeya Problem in Finite Fields SIAM Journal on ...

Web29 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 ... 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 … grant township fire department michigan

An improved lower bound on the size of Kakeya sets over finite fields

WebWe 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. 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 … Web18 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 number of points in the union of a not-too-flat set ... chipotle gives me diarrhea

THE KAKEYA SET AND MAXIMAL CONJECTURES FOR ALGEBRAIC …

On the size of Kakeya sets in ﬁnite ﬁelds - arXiv

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. Web1 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). grant township hall newaygoWeb1 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 ... chipotle gilbert town square

"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

On the size of kakeya sets in finite fields

Improved lower bound on the size of Kakeya sets over 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 ... 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.

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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. 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: …

WebKAKEYA-TYPE SETS IN LOCAL FIELDS WITH FINITE RESIDUE FIELD - Volume 62 Issue 2. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. ... On the size of Kakeya sets in finite fields. J. 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 ...

Web15 de ago. de 2024 · 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 that the size of … 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 …

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 $\mathbb {F}_q^n$ …

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 … chipotle gift card trackerWeb1 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 ... chipotle giveawayWeb14 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 … grant township clare miWeb15 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 ... chipotle gift card check baWebDefinition 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]. chipotle gig harborWeb18 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; … grant township hall jeddo miWeb30 de jul. de 2024 · Sharp density bounds on the finite field Kakeya problem @inproceedings{Bukh2024SharpDB, title= ... Improved lower bounds on the size of … grant township il electronics