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Konferencja
RuFiDiM Conference, Russian-Finnish Symposium in Discrete Mathematics (5; 16-19.05. 2017; Turku; Finland)
Języki publikacji
Abstrakty
The notion of scrambling index was firstly introduced by Akelbek and Kirkland in 2009. For a primitive digraph D, it is defined as the smallest positive integer k such that for every pair of vertices u and v of D there exist two directed paths of lengths k to a common vertex w. This notion turned out to be useful for several applications, e. g., to estimate eigenvalues of non-negative primitive stochastic matrices. In 2010 Huang and Liu with the background of a memoryless communication system generalized this notion to λ-tuples of vertices and named it λ-th upper scrambling index. These notions can be reformulated in terms of matrix theory. A standard way to generate matrices with the given λ-th upper scrambling index is to apply certain matrix transformations that preserve this index to the existing examples of matrices with known λ-th upper scrambling index. In this paper we completely characterize bijective linear maps preserving λ-th upper scrambling index 1 or 0.
Słowa kluczowe
Wydawca
Czasopismo
Rocznik
Tom
Strony
119--141
Opis fizyczny
Bibliogr. 11 poz., rys.
Twórcy
autor
- Lomonosov Moscow State University, 119991, Moscow, Russia
- Moscow Center for Continuous Mathematical Education, 119002, Moscow, Russia
- Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Russia
autor
- Lomonosov Moscow State University, 119991, Moscow, Russia
- Moscow Center for Continuous Mathematical Education, 119002, Moscow, Russia
- Moscow Institute of Physics and Technology, 141701, Dolgoprudny, Russia
Bibliografia
- [1] Brualdi RA, Ryser HJ. Combinatorial matrix theory. Encyclopedia of Mathematics and its Applications, vol. 39, Cambridge University Press, Cambridge, 1991. ISBN-10:0521322650, 13:978-0521322652.
- [2] Akelbek M, Kirkland S. Coefficients of ergodicity and scrambling index, Linear Algebra Appl. 2009;430(4):1111-1130. URL https://doi.org/10.1016/j.laa.2008.10.007.
- [3] Paz A. Introduction to Probabilistic Automata, Academic Press, New York, 1971. ISBN-978-0-12-547650-8. doi:10.1016/C2013-0-11297-4.
- [4] Seneta E. Nonnegative Matrices and Markov Chains, Springer-Verlag, New York, 1981. doi:10.1007/0-387-32792-4.
- [5] Huang Y, Liu B. Generalized scrambling indices of a primitive digraph, Linear Algebra Appl. 2010;433(11-12):1798-1808. URL https://doi.org/10.1016/j.laa.2010.06.043.
- [6] Brualdi RA, Liu B. Generalized exponents of primitive directed digraphs, J. Graph Theory 1990;14:483-499. URL https://doi.org/10.1002/jgt.3190140413.
- [7] Frobenius G. Über die Darstellung der endlichen Gruppen durch lineare Substitutionen, Sitzungsber., Preuss. Akad. Wiss. (Berlin), Berlin, 1897, pp. 994-1015.
- [8] Pierce S, et al. A survey of linear preserver problems, Linear and Multilinear Algebra 1992;33(1-2):1-119. URL https://doi.org/10.1080/03081089208818176.
- [9] Guterman AE, Maksaev AM. Maps preserving scrambling index, Linear and Multilinear Algebra 2018;66(4):840-859. URL https://doi.org/10.1080/03081087.2017.1329814.
- [10] Beasley LB, Guterman AE. The characterization of operators preserving primitivity for matrix k-tuples, Linear Algebra Appl. 2009;430:1762-1777. URL https://doi.org/10.1016/j.laa.2008.06.031.
- [11] Beasley LB, Pullman NJ. Linear operators that strongly preserve primitivity, Linear and Multilinear Algebra, 1989;25(3):205-213. URL https://doi.org/10.1080/03081088908817942.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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