DOI QR코드

DOI QR Code

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)
  • 발행 : 2005.05.01

초록

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 $SIB_n\;and\;class\;IB_n$.

키워드

참고문헌

  1. Z. Bo, Weak exponent of indecomposability of an irreducible Boolean matrix, Ars Combin. 60 (2001), 59-63
  2. R. A. Brualdi and B. Liu, Fully indecomposable exponents of primitive matrices, Proc. Amer. Math. Soc. 112 (1991), 1193-1201
  3. R. A. Brualdi, Hall exponents of Boolean matrices, Czechoslovak Math. J. 40 (1990), 659-670
  4. R. A. Brualdi and H. J. Ryser, Combinatorial Matrix Theory, Cambridge Uni- versity Press, Cambridge, 1991
  5. M. Lewin, On exponents of primitive matrices, Numer. Math. 18 (1971), 154-161 https://doi.org/10.1007/BF01436324
  6. M. Lewin and Y. Vitek, A system of gaps in the exponent set of primitive ma- trices, Illinois J. Math. 25 (1981), 87-98
  7. B. Liu, On exponent of indecomposability for primitive Boolean matrices, Linear Algebra Appl. 298 (1999), 1-8 https://doi.org/10.1016/S0024-3795(99)00082-8
  8. B. Liu, On fully indecomposable exponent for primitive Boolean matrices with symmetric ones, Linear Multilinear Algebra 31 (1992), 131-138 https://doi.org/10.1080/03081089208818129
  9. B. Liu, Weak exponents of irreducible matrices, J. Math. Res. Exposition 14 (1994), 35-41
  10. B. Liu and Z. Bo, On the Hall exponent of Boolean matrices, Linear Algebra Appl. 46 (1999), 165-175 https://doi.org/10.1080/03081089908818611
  11. J. Y. Shao, On a conjecture about the exponent set of primitive matrices, Linear Algebra Appl. 65 (1985), 91-123 https://doi.org/10.1016/0024-3795(85)90090-4
  12. J. Shen, D. Gregory, and S. Neufeld, Exponents of indecomposability, Linear Algebra Appl. 288 (1999), 229-241 https://doi.org/10.1016/S0024-3795(98)10213-6
  13. K. M. Zhang, On Lewin and Vitek's conjecture about the exponent set of primitive matrices, Linear Algebra Appl. 96 (1987), 101{108