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Zap. Nauchn. Sem. POMI, 2014, Volume 428, Pages 13–31 (Mi znsl6049)  

This article is cited in 3 scientific papers (total in 3 papers)

Combinatorial properties of entire semigroups of nonnegative matrices

Yu. A. Al'pina, V. S. Al'pinab

a Kazan (Volga Region) Federal University, Kazan, Russia
b Kazan National Research Technological University, Kazan, Russia

Abstract: Generalizations of the Protasov–Voynov theorem on the structure of irreducible semigroups of nonnegative matrices free of zero rows and columns are obtained. The theorem is extended to semigroups that are allowed to be reducible and to matrices that may have zero columns. The main results concern the semigroups called entire. In the definitions and proofs, only combinatorial properties of nonnegative matrices are exploited.

Key words and phrases: Frobenius form, nonnegative matrix, semigroup.

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English version:
Journal of Mathematical Sciences (New York), 2015, 207:5, 674–685

Document Type: Article
UDC: 512.6
Received: 06.10.2014

Citation: Yu. A. Al'pin, V. S. Al'pina, “Combinatorial properties of entire semigroups of nonnegative matrices”, Computational methods and algorithms. Part XXVII, Zap. Nauchn. Sem. POMI, 428, POMI, St. Petersburg, 2014, 13–31; J. Math. Sci. (N. Y.), 207:5 (2015), 674–685

Citation in format AMSBIB
\Bibitem{AlpAlp14}
\by Yu.~A.~Al'pin, V.~S.~Al'pina
\paper Combinatorial properties of entire semigroups of nonnegative matrices
\inbook Computational methods and algorithms. Part~XXVII
\serial Zap. Nauchn. Sem. POMI
\yr 2014
\vol 428
\pages 13--31
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6049}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2015
\vol 207
\issue 5
\pages 674--685
\crossref{https://doi.org/10.1007/s10958-015-2390-9}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84949623643}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Yu. A. Al'pin, V. S. Al'pina, “Combinatorial and spectral properties of semigroups of stochastic matrices”, J. Math. Sci. (N. Y.), 216:6 (2016), 730–737  mathnet  crossref  mathscinet
    2. Yu. A. Al'pin, V. S. Al'pina, “Locally strongly primitive semigroups of nonnegative matrices”, J. Math. Sci. (N. Y.), 224:6 (2017), 815–820  mathnet  crossref  mathscinet
    3. Yu. A. Alpin, V. S. Alpina, “Indeksy imprimitivnosti temporalnykh komponent polugruppy neotritsatelnykh matrits”, Chislennye metody i voprosy organizatsii vychislenii. XXXI, Zap. nauchn. sem. POMI, 472, POMI, SPb., 2018, 17–30  mathnet
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