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Article Number of Pseudo–anosov Elements in the Mapping Class Group of a Four–holed Sphere(2010) Ozan, Ferihe Atalan; Korkmaz, MustafaWe compute the growth series and the growth functions of reducible and pseudo-Anosov elements of the pure mapping class group of the sphere with four holes with respect to a certain generating set. We prove that the ratio of the number of pseudo-Anosov elements to that of all elements in a ball with center at the identity tends to one as the radius of the ball tends to infinity.
