论文标题
两分尖的图的盛开培养图和任何表面的一般图的参数合理性
Blossoming bijection for bipartite pointed maps and parametric rationality of general maps of any surface
论文作者
论文摘要
我们在任意表面$ \ mathbb {s} $的两分尖头图与相同表面的特定单细胞开花地图之间构造了一个明确的培训。我们的双眼可以访问所有面部的程度，并在初始地图中与尖头顶点的距离。主要结构概括了第二作者的最新工作，该作者涵盖了可定向表面的情况。 我们的培训产生了有关其面部和顶点数量的参数生成一系列图的参数合理性结果的第一个组合证明。特别是，在可定向和不可定向的地图的情况下，它对上述双变量参数生成系列之间的结构差异提供了组合解释。
We construct an explicit bijection between bipartite pointed maps of an arbitrary surface $\mathbb{S}$, and specific unicellular blossoming maps of the same surface. Our bijection gives access to the degrees of all the faces, and distances from the pointed vertex in the initial map. The main construction generalizes recent work of the second author which covered the case of an orientable surface. Our bijection gives rise to a first combinatorial proof of a parametric rationality result concerning the bivariate generating series of maps of a given surface with respect to their numbers of faces and vertices. In particular, it provides a combinatorial explanation of the structural difference between the aforementioned bivariate parametric generating series in the case of orientable and non-orientable maps.
