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Counting quasiplatonic cyclic group Actions of Order n

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No logo availableBanff International Research Station (BIRS) for Mathematical Innovation and Discovery
 Camacho, Charles

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Counting quasiplatonic cyclic group Actions of Order n
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Counting quasiplatonic cyclic n-gonal surfaces
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17
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You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Abstract
Define QC$(n)$ to be the number of isomorphisms classes of quasiplatonic cyclic $n$-gonal surfaces. We use formulas of R.\ Benim and A.\ Wootton to describe a method for computing QC$(n)$. We also relate QC$(n)$ to the number of regular dessins d'enfants having a cyclic group of automorphisms of order $n$.