Geodesic
Combinatorial properties of irreducible semigroups of nonnegative matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXV, Tome 405 (2012), pp. 13-23 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper suggests a combinatorial proof of the Protasov–Voynov theorem on an irreducible semigroup of nonnegative matrices free of positive matrices. This solves the problem posed by the authors of the theorem. 
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Yu. A. Al'pin; V. S. Al'pina. Combinatorial properties of irreducible semigroups of nonnegative matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXV, Tome 405 (2012), pp. 13-23. http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a1/

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