Permutations with restricted movement

A restricted permutation of a locally finite directed graph $ G = (V, E) is vertex \pi: V\to V for which (v, \pi(v))\in E $, any v\in $. The set such permutations, denoted by \Omega(G) with group action induced from subset isomorphisms form topological dynamical system. We focus on the particular case presented Schmidt and Strasser [18] {\mathbb Z}^d in subshift type. show correspondence between permutations perfect matchings (also known as dimer coverings). use this order to investigate compute entropy class cases $-permutations. discuss global local admissibility patterns, context Finally, we review related models injective surjective functions.