论文标题
2-均匀的环形图，分类和渐近行为
2-uniform toroidal maps, classification and asymptotic behavior
论文作者
论文摘要
如果地图具有受汽车群体作用的顶点的k传输类别，则据说它是k-均匀的。圆环上1-均匀图的分类是已知的。在本文中，我们将圆环上的2-均匀图分类为同构。这些地图的组合类型数量的显式公式是根据数字理论（例如除数函数）在数量理论中获得的算术函数。还讨论了这些功能的渐近行为，因为顶点的数量倾向于无穷大，我们获得了连续的函数，这些功能渐近地用作上限和下限。
If a map has k transitivity classes of vertices that are subject to the action of the automorphism group, it is said to be k-uniform. The classification of 1-uniform maps on the torus is known. In this article, we classify 2-uniform maps on the torus up to isomorphism. Explicit formulas for the number of combinatorial types of these maps on number of vertices is obtained in terms of arithmetic functions in number theory, such as the divisor function. The asymptotic behaviour of these functions as number of vertices tends to infinity is also discussed and we obtained continuous functions which asymptotically served as upper and lower bounds.
