标题： 平面图和棱柱形铺砌 显示英文标题

标题： Plabic graphs and zonotopal tilings

摘要： 我们说两个集合$S,T\subset\{1,2,\dots,n\}$是弦分离的，如果不存在满足$a,b,c,d$的循环有序整数四元组$a,c\in S-T$和$b,d\in T-S$。这是 Leclerc 和 Zelevinsky 的弱分离的一个较弱版本。我们证明了每个按包含关系最大的两两弦分离集合的集合也按大小最大。此外，我们证明了这样的集合恰好是三维循环棱柱体的精细棱柱镶嵌的顶点标签集合。在我们的构造中，plabic 图和平方变换分别作为棱柱镶嵌的水平截面及其变异自然出现。 显示英文摘要

摘要： We say that two sets $S,T\subset\{1,2,\dots,n\}$ are chord separated if there does not exist a cyclically ordered quadruple $a,b,c,d$ of integers satisfying $a,c\in S-T$ and $b,d\in T-S$. This is a weaker version of Leclerc and Zelevinsky's weak separation. We show that every maximal by inclusion collection of pairwise chord separated sets is also maximal by size. Moreover, we prove that such collections are precisely vertex label collections of fine zonotopal tilings of the three-dimensional cyclic zonotope. In our construction, plabic graphs and square moves appear naturally as horizontal sections of zonotopal tilings and their mutations respectively.