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Fundamentalnaya i Prikladnaya Matematika, 2007, Volume 13, Issue 6, Pages 35–112 (Mi fpm1088)  
This article is cited in 18 scientific papers (total in 18 papers)

Catalog of dessins d'enfants with no more than 4 edges

N. M. Adrianova, N. Ya. Amburgb, V. A. Dremova, Yu. Yu. Kochetkovc, E. M. Kreinesa, Yu. A. Levitskayaa, V. F. Nasretdinovab, G. B. Shabatd

a M. V. Lomonosov Moscow State University
b Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
c Moscow State Institute of Electronics and Mathematics (Technical University)
d Russian State University for the Humanities
Full-text PDF (980 kB) Citations (18)
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Abstract: In this work, all the dessins d'enfants with no more than 4 edges are listed and their Belyi pairs are computed. In order to enumerate all dessins, the technique of matrix model computations was used. The total number of dessins is 134; among them 77 are spherical, 53 of genus 1, and 4 of genus 2. The automorphism groups of all the dessins are also found. Dessins are listed by the number of edges. Dessins with the same number of edges are ordered lexicographically by their lists of 0-valencies. The corresponding matrix model for any list of 0-valencies is given and computed. Complex matrix models for dessins with 1–3 edges are used. For the dessins with 4 edges, we use Hermitian matrix model.
English version:
Journal of Mathematical Sciences (New York), 2009, Volume 158, Issue 1, Pages 22–80
DOI: https://doi.org/10.1007/s10958-009-9373-7
Bibliographic databases:
UDC: 511.6+512.7+519.17
Language: Russian
Citation: N. M. Adrianov, N. Ya. Amburg, V. A. Dremov, Yu. Yu. Kochetkov, E. M. Kreines, Yu. A. Levitskaya, V. F. Nasretdinova, G. B. Shabat, “Catalog of dessins d'enfants with no more than 4 edges”, Fundam. Prikl. Mat., 13:6 (2007), 35–112; J. Math. Sci., 158:1 (2009), 22–80
Citation in format AMSBIB
\Bibitem{AdrAmbDre07}
\by N.~M.~Adrianov, N.~Ya.~Amburg, V.~A.~Dremov, Yu.~Yu.~Kochetkov, E.~M.~Kreines, Yu.~A.~Levitskaya, V.~F.~Nasretdinova, G.~B.~Shabat
\paper Catalog of dessins d'enfants with no more than 4~edges
\jour Fundam. Prikl. Mat.
\yr 2007
\vol 13
\issue 6
\pages 35--112
\mathnet{http://mi.mathnet.ru/fpm1088}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2476028}
\transl
\jour J. Math. Sci.
\yr 2009
\vol 158
\issue 1
\pages 22--80
\crossref{https://doi.org/10.1007/s10958-009-9373-7}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-62249214936}
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  • https://www.mathnet.ru/eng/fpm/v13/i6/p35
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Фундаментальная и прикладная математика
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