On the size of kakeya sets in finite fields

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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) … 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 ...

THE KAKEYA SET AND MAXIMAL CONJECTURES FOR ALGEBRAIC …

Web1 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 ... 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 ... circo safari bedding collection

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

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 … 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 … diamond car symbol

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

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 … diamond cart shopperWeb18 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 ... diamond car sticker

"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]. " - On the size of kakeya sets in finite fields

On the size of kakeya sets in finite fields

On the Size of Kakeya Sets in Finite Vector Spaces

Web30 de jul. de 2024 · Sharp density bounds on the finite field Kakeya problem @inproceedings{Bukh2024SharpDB, title= ... Improved lower bounds on the size of … 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 …

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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 …

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 ... WebCiteSeerX - 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 …

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 … 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 …

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

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 … circor weihaiWebOn 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 … circo sandal washing instructionsWebA 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 … circos analysisWebIn 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 ... diamond cartridge 4 gramsWebA 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 … circos housekeepingWebON THE SIZE OF KAKEYA SETS IN FINITE FIELDS ZEEVDVIR 1.Introduction Let𝔽denoteaﬁniteﬁeldof𝑞elements.AKakeya set(alsocalledaBesicovitch … diamond carved ringWebAbstract. 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 … diamond cartier watch price