广义渗流格的对偶与最外有界性
Duality and Outermost Boundaries in Generalized Percolation Lattices
摘要：
在本文中，我们考虑一个连通的可平面图$G$和施加的条件，导致$G$具有渗流格状细胞结构。假设$G$的每个胞元是被占用的或空的，我们描述了$G$中星连通分支和正连通分支的最外边界。然后，我们考虑的对偶图的$G$和施加的条件下，对偶也是一个渗流格。最后，利用$G$及其对偶，我们构造了围绕被占据组分的空胞环，并研究了矩形中的左右交叉和键渗流。
英文摘要：
In this paper we consider a connected planar graph $G$ and impose conditions that results in $G$ having a percolation lattice-like cellular structure. Assigning each cell of $G$ to be either occupied or vacant, we describe the outermost boundaries of star and plus connected components in $G$. We then consider the dual graph of $G$ and impose conditions under which the dual is also a percolation lattice. Finally, using $G$ and its dual, we construct vacant cell cycles surrounding occupied components and study left right crossings and bond percolation in rectangles.
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