Sets of weak exponents of indecomposability for irreducible Boolean matrices
Bull. Korean Math. Soc. 2005 Vol. 42, No. 2, 415-420
Published online June 1, 2005
Zhou Bo, Han Hyuk Cho, and Suh-Ryung Kim
South China Normal University, Seoul National University, Seoul National University
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
MSC numbers : 05C20, 15A33
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