Abstract
Riemann’s Existence Theorem gives the following bijections:
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(1)
Isomorphism classes of Belyi maps of degree d.
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(2)
Equivalence classes of generating systems of degree d.
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(3)
Isomorphism classes of dessins d’enfants with d edges.
In previous work, the first author and collaborators exploited the correspondence between Belyi maps and their generating systems to provide explicit equations for two infinite families of dynamical Belyi maps. We complete this picture by describing the dessins d’enfants for these two families.
MM partially supported by the Simons Foundation grant #359721.
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References
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Manes, M., Melamed, G., Tobin, B. (2019). Dessins D’enfants for Single-Cycle Belyi Maps. In: Balakrishnan, J., Folsom, A., Lalín, M., Manes, M. (eds) Research Directions in Number Theory. Association for Women in Mathematics Series, vol 19. Springer, Cham. https://doi.org/10.1007/978-3-030-19478-9_7
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DOI: https://doi.org/10.1007/978-3-030-19478-9_7
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