The number of nonseparable maps on the projective plane |
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Authors: | Zhao-xiang Li Li-ying Mou Fen Lei Jie Xu |
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Institution: | 1. Department of Mathematics, Minzu University of China, Beijing, 100081, China
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Abstract: | In this paper, we study the rooted nonseparable maps on the sphere and the projective plane with the valency of root-face
and the number of edges as parameters. Explicit expression of enumerating functions are obtained for such maps on the sphere
and the projective plane. A parametric expression of the generating function is obtained for such maps on the projective plane,
from which asymptotic evaluations are derived. Moreover, if the number of edges is sufficiently large, then almost all nonseparable
maps on the projective plane are not triangulation. |
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Keywords: | Nonseparable maps Enumerating function Asymptotic evaluation |
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