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Sbornik: Mathematics, 2016, Volume 207, Issue 5, Pages 639–651
DOI: https://doi.org/10.1070/SM8567 (Mi sm8567) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Combinatorial structure of $k$-semiprimitive matrix families

Yu. A. Al'pina, V. S. Al'pinab

a Kazan (Volga Region) Federal University
b Kazan National Research Technological University
English version PDF (459 kB) Citations (1)
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DOI: https://doi.org/10.1070/SM8567
Abstract: Protasov's Theorem on the combinatorial structure of $k$-primitive families of non-negative matrices is generalized to $k$-semiprimitive matrix families. The main tool is the binary relation of colour compatibility on the vertices of the coloured graph of the matrix family.
Bibliography: 14 titles.
Keywords: nonnegative matrices, Perron-Frobenius Theorem, coloured graphs.
Received: 08.07.2015 and 19.10.2015
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 5, Pages 3–16
DOI: https://doi.org/10.4213/sm8567
Bibliographic databases:
Document Type: Article
UDC: 512.643.8
MSC: Primary 15B48; Secondary 15A30, 20M15
Language: English
Original paper language: Russian
Citation: Yu. A. Al'pin, V. S. Al'pina, “Combinatorial structure of $k$-semiprimitive matrix families”, Mat. Sb., 207:5 (2016), 3–16; Sb. Math., 207:5 (2016), 639–651
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian version PDF:82
    English version PDF:21
    References:90
    First page:42
     
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