Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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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)
  • Published : 2005.05.01
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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 $SIB_n\;and\;class\;IB_n$.

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References

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