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The number of rooted Eulerian planar maps
Authors:JunLiang Cai  YanPei Liu
Institution:(1) School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University, Beijing, 100875, China;(2) Department of Mathematics, Beijing Jiaotong University, Beijing, 100044, China
Abstract:In this paper we provide a solution of the functional equation unsolved in the paper, by the second author, “On functional equations arising from map enumerations” that appeared in Discrete Math, 123: 93–109 (1993). It is also the number of combinatorial distinct rooted general eulerian planar maps with the valency of root-vertex, the number of non-root vertices and non-root faces of the maps as three parameters. In particular, a result in the paper, by the same author, “On the number of eulerian planar maps” that appeared in Acta Math Sinica, 12: 418–423 (1992) is simplified. This work was supported by the National Natural Science Foundation of China (Grant No. 10271017)
Keywords:Eulerian map  functional equation  Lagrangian inversion
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