On the size of kakeya sets in finite fields

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August undefined, 2024

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 …

Conical Kakeya and Nikodym sets in finite fields Request PDF

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. Web30 de jul. de 2024 · Finite field Kakeya and Nikodym sets in three dimensions. SIAM J. Discrete Math., 32(4):2836-2849, 2024. arXiv:1609.01048. An improved lower bound on the size of Kakeya sets over finite fields floral diamond painting kits

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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 every Kakeya set is of size at least Cn·q … 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> 0, that the size of every Kakeya set is … great sci fi authors

Conical Kakeya and Nikodym sets in finite fields - ScienceDirect

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 … 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. great sci fi audio booksWeb29 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 ... great scientists of history

"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 … " - On the size of kakeya sets in finite fields

On the size of kakeya sets in finite fields

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

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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 ... 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 C n ⋅ q …

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 … Web16 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) …

WebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS ZEEVDVIR 1.Introduction Let𝔽denoteaﬁniteﬁeldof𝑞elements.AKakeya set(alsocalledaBesicovitch … 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 …

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: …

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 ... floral dish italy t26WebA 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 n−1, where Cn depends only on n. This improves the previously best lower bound for general n of ≈ q 4n/7 due to Mockenhaupt and Tao (Duke Math. J. 2004). 1 great sci fi authors larry nivenWeb18 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; … great sci fi authors anne mccaffreyWeb10 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. floral dish drying matWebDefinition 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]. great sci fi authors isaac asimovWebA 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 … floral dishes setWebSaraf 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. floral dishware