SETS OF WEAK EXPONENTS OF INDECOMPOSABILITY FOR IRREDUCIBLE BOOLEAN MATRICES

Title & Authors
SETS OF WEAK EXPONENTS OF INDECOMPOSABILITY FOR IRREDUCIBLE BOOLEAN MATRICES
BO, ZHOU; CHO, HAN-HYUK; KIM, SUH-RYUNG;

Abstract
Let $\small{IB_n}$ be the set of all irreducible matrices in $\small{B_n}$ and let $\small{SIB_n}$ be the set of all symmetric matrices in $\small{IB_n}$. Finding an upper bound for the set of indices of matrices in $\small{IB_n}$ and $\small{SIB_n}$ and determining gaps in the set of indices of matrices in $\small{IB_n}$ and $\small{SIB_n}$ 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 $\small{SIB_n\;and\;IB_n}$, and show that there does not exist a gap in the set of weak exponents of indecomposability for any of class $\small{SIB_n\;and\;class\;IB_n}$.
Keywords
Boolean matrices;weak exponents of indecomposability;
Language
English
Cited by
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