Geodesic
Ribbon Graphs and Belyi Pairs with Partially Prescribed Branching
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 177-188

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Given a ribbon graph of arbitrary genus, we construct a spherical graph with the same two columns of the passport. And given a spherical graph, we present an algorithm for constructing a graph with the two columns of the same passport and any admissible genus. We also discuss possible applications to the theory of dessins d'enfants.
Keywords: Belyi pairs, ribbon graphs
Mots-clés : monodromy. 
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     author = {Vik. S. Kulikov and G. B. Shabat},
     title = {Ribbon {Graphs} and {Belyi} {Pairs} with {Partially} {Prescribed} {Branching}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {177--188},
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     volume = {320},
     year = {2023},
     language = {ru},
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Vik. S. Kulikov; G. B. Shabat. Ribbon Graphs and Belyi Pairs with Partially Prescribed Branching. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Algebra and Arithmetic, Algebraic, and Complex Geometry, Tome 320 (2023), pp. 177-188. http://geodesic.mathdoc.fr/item/TM_2023_320_a7/