Enumeration on Nonseparable Planar Maps |
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| Authors: | Junliang Cai |
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| Affiliation: | a Department of Mathematics, Beijing Normal University, Beijing 100875, People’s Republic of China;b Department of Mathematics, Northern Jiaotong University, Beijing 100044, People’s Republic of Chinaf1 |
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| Abstract: | This paper provides some functional equations satisfied by the generating functions for nonseparable rooted planar maps with the valency of root-vertex, the number of edges and the valency of root-faces of the maps as three parameters. But the solutions of these equations can only be obtained indirectly by considering some relations between nonseparable and general rooted planar maps. One of them is an answer to the open problem 6.1 in Liu (1983, Comb. Optim. CORR83-26, University of Waterloo). |
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