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 | |
【 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.
【 授权许可】
Free
【 预 览 】
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