On the size of kakeya sets in finite fields

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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 … 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 …

An improved lower bound on the size of Kakeya sets over 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, for any ǫ> 0, that the size of every Kakeya set is … 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 ... daily themed crossword october 5 2021

On the size of Kakeya sets in finite fields - ResearchGate

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. 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 … 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 $\mathbb {F}_q^n$ … daily themed crossword october 17 2022

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(PDF) Size of local finite field Kakeya sets - ResearchGate

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 … 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 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 bionaire ultrasonic humidifier bu498Web10 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 … daily themed crossword pottermania

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

On the size of kakeya sets in finite fields

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

WebON 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]. 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].

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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 … 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 ...

Web1 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 ... 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).

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 …

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 ...

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 bionaire ultrasonic humidifier cleaningWebobservation 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. bionaire w12WebDive 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 … daily themed crossword pottermania packWebSaraf 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. daily themed crossword puzzle answers may 17Web16 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 … daily themed mini answersWeb22 de fev. de 2013 · On the size of Kakeya sets in finite vector spaces. 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 … bionaire warm mist humidifier ebayWeb30 de jul. de 2024 · Sharp density bounds on the finite field Kakeya problem @inproceedings{Bukh2024SharpDB, title= ... Improved lower bounds on the size of … bionaire w7 parts