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This article is cited in 6 scientific papers (total in 6 papers)
Combinatorial description of a moduli space of curves and of
extremal polynomials
A. B. Bogatyrev
Institute of Numerical Mathematics, Russian Academy of Sciences
Abstract:
For the description of extremal polynomials (that is, the typical solutions
of least deviation problems) one uses real hyperelliptic curves.
A partitioning of the moduli space of such curves into cells enumerated by
trees is considered. As an application of these techniques
the range of the period map of the universal cover of the moduli space
is explicitly calculated. In addition, extremal polynomials are enumerated
by weighted graphs.
DOI:
https://doi.org/10.4213/sm772
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English version:
Sbornik: Mathematics, 2003, 194:10, 1451–1473
Bibliographic databases:
    
UDC:
517.545+517.518.826
MSC: 30F60, 14H15, 41A50
Received: 25.12.2001 and 17.11.2002
Citation:
A. B. Bogatyrev, “Combinatorial description of a moduli space of curves and of
extremal polynomials”, Mat. Sb., 194:10 (2003), 27–48; Sb. Math., 194:10 (2003), 1451–1473
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/msb772https://doi.org/10.4213/sm772 http://mi.mathnet.ru/eng/msb/v194/i10/p27
Citing articles on Google Scholar:
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This publication is cited in the following articles:
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Bogatyrev A., “Effective computation of optimal stability polynomials”, Calcolo, 41:4 (2004), 247–256
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A. B. Bogatyrev, “Effective solution of the problem of the optimal stability polynomial”, Sb. Math., 196:7 (2005), 959–981
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Franz Peherstorfer, Klaus Schiefermayr, “Description of Inverse Polynomial Images which Consist of Two Jordan Arcs with the Help of Jacobi’s Elliptic Functions”, Comput. Methods Funct. Theory, 4:2 (2005), 355
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Eremenko A. Yuditskii P., “Comb Functions”, Recent Advances in Orthogonal Polynomials, Special Functions, and their Applications, Contemporary Mathematics, 578, ed. Arvesu J. Lagomasino G., Amer Mathematical Soc, 2011, 99–118
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Moale I. Yuditskii P., “Spectral Sets of Periodic Matrices Related To the Strong Moment Problem”, J. Spectr. Theory, 4:1 (2014), 23–52
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A. B. Bogatyrev, “Combinatorial analysis of the period mapping: the topology of 2D fibres”, Sb. Math., 210:11 (2019), 1531–1562
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