Equal entries in totally positive matrices

被引：4
|
作者：
Farber, Miriam [1 ]
Faulk, Mitchell [2 ]
Johnson, Charles R. [3 ]
Marzion, Evan [4 ]
机构：
[1] Technion Israel Inst Technol, Dept Math, IL-32000 Haifa, Israel
[2] Univ Notre Dame, Dept Math, Notre Dame, IN 46556 USA
[3] Coll William & Mary, Dept Math, Williamsburg, VA 23187 USA
[4] Univ Wisconsin, Dept Math, Madison, WI 53706 USA
来源：
LINEAR ALGEBRA AND ITS APPLICATIONS | 2014年 / 454卷
基金：
美国国家科学基金会;
关键词：
Totally positive matrices; Point-line incidences; Bruhat order of permutations; Outerplanar graphs;
D O I：
10.1016/j.laa.2014.04.007
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show that the maximal number of equal entries in a totally positive (resp. totally nonsingular) n-by-n matrix is theta(n(4/3)) (resp. theta(n(3/2))). Relationships with point-line incidences in the plane, Bruhat order of permutations, and TP completability are also presented. We also examine the number and positionings of equal 2-by-2 minors in a 2-by-n TP matrix, and give a relationship between the location of equal 2-by-2 minors and outerplanar graphs. (C) 2014 Elsevier Inc. All rights reserved.
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收藏
页码：91 / 106
页数：16
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