期刊论文详细信息
JOURNAL OF COMBINATORIAL THEORY SERIES A 卷:165
Blossoming bijection for higher-genus maps
Article
Lepoutre, Mathias1 
[1] Ecole Polytech, LIX, 1 Rue Honore Estiennes Orves, F-91120 Palaiseau, France
关键词: Combinatorics;    Bijection;    Maps;    Higher genus;    Blossoming tree;    Rationality;   
DOI  :  10.1016/j.jcta.2019.01.005
来源: Elsevier
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【 摘 要 】

In 1997, Schaeffer described a bijection between Eulerian planar maps and some trees. In this work we generalize his work to a bijection between maps on an orientable surface of any fixed genus and some unicellular maps with the same genus. An important step of this construction is to exhibit a canonical orientation for maps, that allows to apply the same local opening algorithm as Schaeffer did. As an important byproduct, we obtain the first bijective proof of a result of Bender and Canfield from 1991, when they proved that the generating series of maps in higher genus is a rational function of the generating series of planar maps. (C) 2019 Elsevier Inc. All rights reserved.

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