Planar Maps as Labeled Mobiles
Planar Maps as Labeled Mobiles
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DOI：
10.37236/1822
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发表时间：
2004-05
期刊：
影响因子：
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通讯作者：
J. Bouttier;P. Francesco;E. Guitter
中科院分区：
文献类型：
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作者：
J. Bouttier;P. Francesco;E. Guitter
我们延长Schaeffer的双射之间的有根四边形和标记树的一般情况下，欧拉平面地图与规定的脸价，以获得一个双射与一类新的标记树，我们称之为手机。我们的双射涵盖了所有类别的地图，以前列举的两个矩阵模型所使用的物理学家或双射与组合学家使用的开花树。我们的双射减少了枚举的地图，更简单的是，手机，而且保持跟踪的测地距离内的初始地图通过手机的标签。生成函数的手机服从系统的代数递归关系。
We extend Schaeffer's bijection between rooted quadrangulations and well-labeled trees to the general case of Eulerian planar maps with prescribed face valences to obtain a bijection with a new class of labeled trees, which we call mobiles. Our bijection covers all the classes of maps previously enumerated by either the two-matrix model used by physicists or by the bijection with blossom trees used by combinatorists. Our bijection reduces the enumeration of maps to that, much simpler, of mobiles and moreover keeps track of the geodesic distance within the initial maps via the mobiles' labels. Generating functions for mobiles are shown to obey systems of algebraic recursion relations.