Collinear points in permutations

被引：1

作者：

Cooper, Joshua N. ^{[1
]}

Solymosi, Jozsef

机构：

[1] NYU, Courant Inst Math Sci, Dept Math, New York, NY 10012 USA

[2] Univ British Columbia, Dept Math, Vancouver, BC, Canada

来源：

ANNALS OF COMBINATORICS | 2005年 / 9卷 / 02期

关键词：

finite field; affine geometry; collinearity; transversal;

D O I：

10.1007/s00026-005-0248-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider the following problem: how many collinear triples of points must a transversal of Z(n) x Z(n) have? This question is connected with venerable issues in discrete geometry. We show that the answer, for n prime, is between (n - 1) = 4 and (n - 1) /2, and consider an analogous question for collinear quadruples. We conjecture that the upper bound is the truth and suggest several other interesting problems in this area.

引用

页码：169 / 175

页数：7