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

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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. 
@article{ZNSL_2012_405_a1,
     author = {Yu. A. Al'pin and V. S. Al'pina},
     title = {Combinatorial properties of irreducible semigroups of nonnegative matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--23},
     publisher = {mathdoc},
     volume = {405},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a1/}
}
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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/