[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/BKMS.2005.42.2.415

SETS OF WEAK EXPONENTS OF INDECOMPOSABILITY FOR IRREDUCIBLE BOOLEAN MATRICES

BO, ZHOU (DEPARTMENT OF MATHEMATICS, SOUTH CHINA NORMAL UNIVERSITY)
CHO, HAN-HYUK (DEPARTMENT OF MATHEMATICS EDUCATION, SEOUL NATIONAL UNIVERSITY)
KIM, SUH-RYUNG (DEPARTMENT OF MATHEMATICS EDUCATION, SEOUL NATIONAL UNIVERSITY)

Publication Information

Bulletin of the Korean Mathematical Society / v.42, no.2, 2005 , pp. 415-420 More about this Journal

Abstract

Let $IB_n$ be the set of all irreducible matrices in $B_n$ and let $SIB_n$ be the set of all symmetric matrices in $IB_n$ . Finding an upper bound for the set of indices of matrices in $IB_n$ and $SIB_n$ and determining gaps in the set of indices of matrices in $IB_n$ and $SIB_n$ has been studied by many researchers. In this paper, we establish a best upper bound for the set of weak exponents of indecomposability of matrices in $SIB_n\;and\;IB_n$ , and show that there does not exist a gap in the set of weak exponents of indecomposability for any of class $SIB_n\;and\;class\;IB_n$ .

Keywords

Boolean matrices; weak exponents of indecomposability;

Citations & Related Records

Reference

1	B. Liu, Weak exponents of irreducible matrices, J. Math. Res. Exposition 14 (1994), 35-41
2	B. Liu and Z. Bo, On the Hall exponent of Boolean matrices, Linear Algebra Appl. 46 (1999), 165-175 DOI ScienceOn
3	J. Y. Shao, On a conjecture about the exponent set of primitive matrices, Linear Algebra Appl. 65 (1985), 91-123 DOI ScienceOn
4	J. Shen, D. Gregory, and S. Neufeld, Exponents of indecomposability, Linear Algebra Appl. 288 (1999), 229-241 DOI ScienceOn
5	M. Lewin and Y. Vitek, A system of gaps in the exponent set of primitive ma- trices, Illinois J. Math. 25 (1981), 87-98
6	B. Liu, On exponent of indecomposability for primitive Boolean matrices, Linear Algebra Appl. 298 (1999), 1-8 DOI ScienceOn
7	R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge Uni- versity Press, Cambridge, 1991
8	Z. Bo, Weak exponent of indecomposability of an irreducible Boolean matrix, Ars Combin. 60 (2001), 59-63
9	R. A. Brualdi and B. Liu, Fully indecomposable exponents of primitive matrices, Proc. Amer. Math. Soc. 112 (1991), 1193-1201
10	R. A. Brualdi, Hall exponents of Boolean matrices, Czechoslovak Math. J. 40 (1990), 659-670
11	B. Liu, On fully indecomposable exponent for primitive Boolean matrices with symmetric ones, Linear Multilinear Algebra 31 (1992), 131-138 DOI
12	K. M. Zhang, On Lewin and Vitek's conjecture about the exponent set of primitive matrices, Linear Algebra Appl. 96 (1987), 101{108
13	M. Lewin, On exponents of primitive matrices, Numer. Math. 18 (1971), 154-161 DOI