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Enumerating near-4-regular maps on the sphere and the torus |
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| Authors: | Han Ren Yanpei Liu |
| Affiliation: | a Department of Mathematics, Suzhou University, Suzhou 215006, People's Republic of China b Department of Mathematics, Northern Jiaotong University, Beijing 100044, People's Republic of China |
| Abstract: | In this paper rooted near-4-regular maps on the plane and the torus are counted with formulae with respect to four parameters: the root valency, the number of edges, the inner faces, and nonroot-vertex loops. In particular, the number of rooted near-4-regular maps on those surfaces with exactly k nonroot-vertex loops is investigated. |
| Keywords: | (Rooted) map Enumerating function Lagrangian inversion |
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