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Mat. Sb., 2003, Volume 194, Number 10, Pages 27–48 (Mi msb772)  

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

Full text: PDF file (423 kB)
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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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Bogatyrev A., “Effective computation of optimal stability polynomials”, Calcolo, 41:4 (2004), 247–256  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. B. Bogatyrev, “Effective solution of the problem of the optimal stability polynomial”, Sb. Math., 196:7 (2005), 959–981  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. 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  crossref  mathscinet
    4. 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  crossref  mathscinet  isi
    5. Moale I. Yuditskii P., “Spectral Sets of Periodic Matrices Related To the Strong Moment Problem”, J. Spectr. Theory, 4:1 (2014), 23–52  crossref  mathscinet  zmath  isi  scopus
    6. A. B. Bogatyrev, “Combinatorial analysis of the period mapping: the topology of 2D fibres”, Sb. Math., 210:11 (2019), 1531–1562  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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