论文标题
限制移动的排列
Permutations with restricted movement
论文作者
论文摘要
本地有限的定向图$ g =（v，e）$的限制排列是一个顶点置换$π：v \ to v $，对于$（v，π（v））在e $中，对于v $中的任何顶点$ v \ in E $。通过$ω（g）$表示的一组排列，从图形同构的子集引起的组动作形成了拓扑动力学系统。我们专注于Schmidt and Strasser（2016）限制的$ \ Mathbb {Z}^D $定位的特定情况，其中$ω（g）$是有限类型的子移动。我们显示限制排列和完美匹配（也称为二聚体覆盖物）之间的对应关系。我们使用此通信来调查和计算一类限制$ \ Mathbb {z}^d $ - permutations的案例中的拓扑熵。在受限的$ \ mathbb {z}^d $ - permutations的背景下，我们讨论了模式的全球和局部可接受性。最后，我们回顾了注射和过滤性限制功能的相关模型。
A restricted permutation of a locally finite directed graph $G=(V,E)$ is a vertex permutation $π: V\to V$ for which $(v,π(v))\in E$, for any vertex $v\in V$. The set of such permutations, denoted by $Ω(G)$, with a group action induced from a subset of graph isomorphisms form a topological dynamical system. We focus on the particular case presented by Schmidt and Strasser (2016) of restricted $\mathbb{Z}^d$ permutations, in which $Ω(G)$ is a subshift of finite type. We show a correspondence between restricted permutations and perfect matchings (also known as dimer coverings). We use this correspondence in order to investigate and compute the topological entropy in a class of cases of restricted $\mathbb{Z}^d$-permutations. We discuss the global and local admissibility of patterns, in the context of restricted $\mathbb{Z}^d$-permutations. Finally, we review the related models of injective and surjective restricted functions.
