On a Furstenberg-Katznelson-Weiss Type Theorem over Finite Fields

被引：6
|
作者：
Le Anh Vinh [1 ]
机构：
[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
来源：
ANNALS OF COMBINATORICS | 2011年 / 15卷 / 03期
关键词：
finite Euclidean graphs; pseudo-random graphs; VECTOR-SPACES; DISTANCE PROBLEM; SETS;
D O I：
10.1007/s00026-011-0107-4
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Using Fourier analysis, Covert, Hart, Iosevich, and Uriarte-Tuero (2008) showed that if the cardinality of a subset of the 2-dimensional vector space over a finite field with q elements is >= rho q(2), with q(-1/2) << rho <= 1 then it contains an isometric copy of >= c rho q(3) triangles. In this note, we give a graph theoretic proof of this result.
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页码：541 / 547
页数：7
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