On the size of kakeya sets in finite fields
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 ... 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
On the size of kakeya sets in finite fields
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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 … 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.
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: … 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 …
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. 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 …
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 $\mathbb {F}_q^n$ …
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 … greene county ohio careersWebAbstract. 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 … greene county ohio building permitsWeb15 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 … greene county ohio ccw renewalWebOn 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 … fluffy but hutWeb22 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 … greene county ohio ccw renewal applicationWeb29 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 ... fluffy but hut signWeb10 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. greene county ohio ccw