论文标题
圆环及其顶点轨道上的一类地图
A class of maps on the torus and their vertex orbits
论文作者
论文摘要
平面的瓷砖（边缘到边缘）是一个瓷砖家族，覆盖平面而没有间隙或重叠。在瓷砖中的顶点的顶点图是该顶点的所有边缘的结合。如果任何两个具有一致顶点数字的顶点相互对称，并且顶点相对于瓷砖的所有对称性组，则瓷砖为$ k $ vertex-hosonos-同质性。在本文中，我们讨论了地图是飞机的$ k $ vertex均匀晶格的商（$ k \ ge 4 $），那么顶点轨道数量的急剧界限。
A tiling (edge-to-edge) of the plane is a family of tiles that cover the plane without gaps or overlaps. Vertex figure of a vertex in a tiling to be the union of all edges incident to that vertex. A tiling is $k$-vertex-homogeneous if any two vertices with congruent vertex figures are symmetric with each other and the vertices form precisely $k$ transitivity classes with respect to the group of all symmetries of the tiling. In this article, we discuss that if a map is the quotient of a plane's $k$-vertex-homogeneous lattice ($k \ge 4$) then what would be the sharp bounds of the number of vertex orbits.
