Bounds on the kth multi-g base index of nearly reducible sign pattern matrices

被引：10

作者：

Li, Qian ^{[2
]}

Liu, Bolian ^{[1
]}

机构：

[1] S China Normal Univ, Dept Math, Guangzhou 510631, Guangdong, Peoples R China

[2] S China Agr Univ, Dept Math, Guangzhou 510640, Peoples R China

来源：

DISCRETE MATHEMATICS | 2008年 / 308卷 / 21期

基金：

中国国家自然科学基金;

关键词：

kth multi-g base index; matrix; generalized sign pattern; irreducible; nearly reducible; cycle; bound;

D O I：

10.1016/j.disc.2007.09.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Li et al. [On the period and base of a sign pattern matrix. Linear Algebra Appl. 212/213 (1994) 101-120.] extended the concepts of the base and period from nonnegative matrices to powerful sign pattern matrices. Then. Shao and You [Bound on the basis of irreducible generalized sign pattern matrices, Linear Algebra Appl. 427 (2007) 285-300.] extended the concepts of the base from powerful sign pattern matrices to non-powerful irreducible sign pattern matrices. In this paper we mainly study the kth multi-g base index for non-powerful primitive nearly reducible sign pattern matrices. We obtain sharp upper bounds, together with a complete characterization of the equality cases of the kth multi-g base index for primitive nearly reducible generalized sign pattern matrices. We also show that there exist "gaps" in the kth multi-g base index set of the classes of such matrices. (c) 2007 Elsevier B.V All rights reserved.

引用

页码：4846 / 4860

页数：15

共 12 条

[1]

Brualdi R. A., 1991, COMBINATORIAL MATRIX, V39

[2] ON THE EXPONENT OF A PRIMITIVE, NEARLY REDUCIBLE MATRIX [J].

BRUALDI, RA ;

ROSS, JA .

MATHEMATICS OF OPERATIONS RESEARCH, 1980, 5 (02) :229-241

[3]

Dulmage A. L., 1967, GRAPH THEORY THEORET, P167

[4]

LEWIN M, 1972, B J LONDON MATH SOC, V5, P75

[5] Irreducible powerful ray pattern matrices [J].

Li, ZS ;

Hall, FJ ;

Stuart, JL .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 342 (1-3) :47-58

[6] ON THE PERIOD AND BASE OF A SIGN PATTERN MATRIX [J].

LI, ZS ;

HALL, F ;

ESCHENBACH, C .

LINEAR ALGEBRA AND ITS APPLICATIONS, 1994, 212 :101-120

[7]

LIU BL, 1996, COMBINATORIAL MATRIX

[8]

LIU BL, 2000, MATRIX COMBINATORICS

[9] Bounds on the base of primitive nearly reducible sign pattern matrices [J].

Liu, Bolian ;

You, Lihua .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2006, 418 (2-3) :863-881

[10] ON THE EXPONENT OF A PRIMITIVE, NEARLY REDUCIBLE MATRIX .2. [J].

ROSS, JA .

SIAM JOURNAL ON ALGEBRAIC AND DISCRETE METHODS, 1982, 3 (03) :395-410

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