A combinatorial version of Sylvester's four-point problem

被引：2

作者：

Warrington, Gregory S. ^{[1
]}

机构：

[1] Univ Vermont, Dept Math & Stat, Burlington, VT 05401 USA

来源：

ADVANCES IN APPLIED MATHEMATICS | 2010年 / 45卷 / 03期

关键词：

JJ Sylvester; Four-point problem; Reduced expressions; Symmetric group; Convex; Probability; Sorting networks; REDUCED DECOMPOSITIONS;

D O I：

10.1016/j.aam.2010.01.008

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

J.J. Sylvester's four-point problem asks for the probability that four points chosen uniformly at random in the plane have a triangle as their convex hull. Using a combinatorial classification of points in the plane due to Goodman and Pollack, we generalize Sylvester's problem to one involving reduced expressions for the long word ill S(n). We conjecture an answer of 1/4 for this new version of the problem. (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：390 / 394

页数：5

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