Ranks of dense alternating sign matrices and their sign patterns

被引：3

作者：

Fiedler, Miroslav ^{[1
]}

Gao, Wei ^{[2
]}

Hall, Frank J. ^{[2
]}

Jing, Guangming ^{[2
]}

Li, Zhongshan ^{[2
]}

Stroev, Mikhail ^{[2
]}

机构：

[1] Acad Sci Czech Republ, Inst Math, CR-11567 Prague 1, Czech Republic

[2] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2015年 / 471卷

关键词：

Alternating sign matrix; Rank; Dense matrix; Sign pattern matrix; Minimum rank; Maximum rank; MINIMUM RANK;

D O I：

10.1016/j.laa.2014.12.034

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, an explicit formula for the ranks of dense alternating sign matrices is obtained. The minimum rank and the maximum rank of the sign pattern of a dense alternating sign matrix are determined. Some related results and examples are also provided. (C) 2015 Elsevier Inc. All rights reserved.

引用

页码：109 / 121

页数：13

共 16 条

[1] Rational realizations of the minimum rank of a sign pattern matrix [J].

Arav, M ;

Hall, FJ ;

Koyuncu, S ;

Li, ZS ;

Rao, B .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2005, 409 :111-125

[2]

Berman A, 2008, ELECTRON J COMB, V15

[3]

Brualdi R.A., 1995, MATRICES SIGN SOLVAB

[4]

Brualdi R.A., 2015, J COMBIN DE IN PRESS

[5]

Brualdi R. A., 1991, Combinatorial Matrix Theory

[6]

Brualdi R.A., 2015, GRAPHS COMB IN PRESS

[7]

Brualdi RA, 2014, AUSTRALAS J COMB, V60, P333

[8] Note on the spectral radius of alternating sign matrices [J].

Brualdi, Richard A. ;

Cooper, Joshua .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2014, 442 :99-105

[9] Patterns of alternating sign matrices [J].

Brualdi, Richard A. ;

Kiernan, Kathleen P. ;

Meyer, Seth A. ;

Schroeder, Michael W. .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2013, 438 (10) :3967-3990

[10] Inverses and eigenvalues of diamond alternating sign matrices [J].

Catral, Minerva ;

Lin, Minghua ;

Olesky, D. D. ;

van den Driessche, P. .

SPECIAL MATRICES, 2014, 2 (01) :78-88

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