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 
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/
@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},
     year = {2012},
     volume = {405},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a1/}
}
TY  - JOUR
AU  - Yu. A. Al'pin
AU  - V. S. Al'pina
TI  - Combinatorial properties of irreducible semigroups of nonnegative matrices
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 13
EP  - 23
VL  - 405
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a1/
LA  - ru
ID  - ZNSL_2012_405_a1
ER  - 
%0 Journal Article
%A Yu. A. Al'pin
%A V. S. Al'pina
%T Combinatorial properties of irreducible semigroups of nonnegative matrices
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 13-23
%V 405
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_405_a1/
%G ru
%F ZNSL_2012_405_a1

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.

[1] V. Yu. Protasov, “Polugruppy neotritsatelnykh matrits”, Uspekhi mat. nauk, 65:6 (2010), 191–192 | DOI | MR | Zbl

[2] V. Yu. Protasov, A. S. Voynov, “Sets of nonnegative matrices without positive products”, Linear Algebra Appl., 437 (2012), 749–765 | DOI | MR | Zbl

[3] V. Romanovsky, “Un théoréme sur les zéros des matrices nonnégatives”, Bull. Soc. Math. France, 61 (1933), 213–219 | MR | Zbl

[4] V. I. Romanovskii, Diskretnye tsepi Markova, Gostekhizdat, M., 1949

[5] H. Minc, Nonnegative Matrices, Wiley, New York, 1988 | MR | Zbl

[6] Yu. A. Alpin, V. S. Alpina, “Teorema Perrona–Frobeniusa: dokazatelstvo s pomoschyu tsepei Markova”, Zap. nauchn. semin. POMI, 359, 2008, 5–16 | Zbl