Geodesic
Locally strongly primitive semigroups of nonnegative matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIX, Tome 453 (2016), pp. 5-14

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The class of locally strongly primitive semigroups of nonnegative matrices is introduced. It is shown that, by a certain permutation similarity, all the matrices of a semigroup of the class considered can be brought to block monomial form; moreover, any matrix product of sufficient length has positive nonzero blocks only. This shows that the following known property of an imprimitive nonnegative matrix in Frobenius form is inherited. If such a matrix is raised to a sufficiently high power, then all its nonzero blocks are positive. A combinatorial criterion of the locally strong primitivity of a semigroup of nonnegative matrices is found. 
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     author = {Yu. A. Al'pin and V. S. Al'pina},
     title = {Locally strongly primitive semigroups of nonnegative matrices},
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     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a0/}
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Yu. A. Al'pin; V. S. Al'pina. Locally strongly primitive semigroups of nonnegative matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXIX, Tome 453 (2016), pp. 5-14. http://geodesic.mathdoc.fr/item/ZNSL_2016_453_a0/