The index set for the class of irreducible Boolean matrices with given period. (English) Zbl 0637.15013

Authors’ summary: We consider the index set \(I_{n,p}\) for the “indices of convergence” of \(n\times n\) irreducible Boolean matrices with period p, which is a generalization of the exponent set \(E_ n\) for the \(n\times n\) primitive matrices. We exhibit a system of gaps in the index set \(I_{n,p}\) and prove that if \(n=rp+s\) with \(0\leq s\leq p-1\), then there are no gaps below \(p([r^ 2-2r+2/4]+1)+5\) for \(r>1\) and no gaps below \(p([r^ 2-2r+2/2]+1)+5\) for \(r\geq 35\).
Reviewer: N.J.Pullman


15B36 Matrices of integers
15B48 Positive matrices and their generalizations; cones of matrices
15B57 Hermitian, skew-Hermitian, and related matrices
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