## 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

### MSC:

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

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