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
收藏
页码：390 / 394
页数：5
相关论文
共 50 条
  • [41] The Four-Point Hypothesis: Transpositions and Complications
    Ormerod, Neil
    IRISH THEOLOGICAL QUARTERLY, 2012, 77 (02) : 127 - 140
  • [42] A laboratory on the four-point probe technique
    Schuetze, AP
    Lewis, W
    Brown, C
    Geerts, WJ
    AMERICAN JOURNAL OF PHYSICS, 2004, 72 (02) : 149 - 153
  • [43] Asymmetric four-point crack specimen
    He, MY
    Hutchinson, JW
    JOURNAL OF APPLIED MECHANICS-TRANSACTIONS OF THE ASME, 2000, 67 (01): : 207 - 209
  • [44] Splines for four-point rational interpolants
    Ramazanov, A-R K.
    Magomedova, V. G.
    TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2016, 22 (04): : 233 - 246
  • [45] Asymmetric four-point crack specimen
    He, M.Y., 1600, ASME, Fairfield, NJ, United States (67):
  • [46] A differential equation for a four-point correlation function in Liouville field theory and elliptic four-point conformal blocks
    Fateev, Vladimir A.
    Litvinov, Alexey V.
    Neveu, Andre
    Onofri, Enrico
    JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2009, 42 (30)
  • [47] Nonlocal Four-Point Boundary Value Problem for the Singularly Perturbed Semilinear Differential Equations
    Robert Vrabel
    Boundary Value Problems, 2011 (1)
  • [48] EXISTENCE OF SOLUTIONS FOR A FOUR-POINT BOUNDARY VALUE PROBLEM OF A NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION
    Dou, Xiaoyan
    Li, Yongkun
    Liu, Ping
    OPUSCULA MATHEMATICA, 2011, 31 (03) : 359 - 372
  • [49] Nonlocal Four-Point Boundary Value Problem for the Singularly Perturbed Semilinear Differential Equations
    Vrabel, Robert
    BOUNDARY VALUE PROBLEMS, 2011,
  • [50] An algebraic combinatorial approach to Sylvester's denumerant
    Xin, Guoce
    Zhang, Chen
    RAMANUJAN JOURNAL, 2025, 66 (04):
12345