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.

引用

页码：91 / 106

页数：16

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