Counting the Number of Quasiplatonic Topological Actions of the Cyclic Group on Surfaces
Abstract
Define QC(n) to be the number of quasiplatonic topological actions of the cyclic group Cn 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 Cn to the number of regular dessins d'enfants having Cn as a group of automorphisms.
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