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Counting the Number of Quasiplatonic Topological Actions of the Cyclic Group on Surfaces
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math.GNmath.COmath.GR
keywords
numberactionsgroupquasiplatonictopologicalcyclicsurfacesaddition
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abstract
Define $QC(n)$ to be the number of quasiplatonic topological actions of the cyclic group $C_n$ on surfaces of genus at least two. We use formulas of Benim and Wootton to give an explicit formula for $QC(n)$. In addition, we relate the number of quasiplatonic topological actions of $C_n$ to the number of regular dessins d'enfants having $C_n$ as a group of automorphisms.
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