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Counting the Number of Quasiplatonic Topological Actions of the Cyclic Group on Surfaces

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arxiv 1811.04042 v1 pith:OYDNJY7N submitted 2018-11-09 math.GN math.COmath.GR

Charles Camacho This is my paper · ORCID
classification 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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