  A restricted permutation of a locally finite directed graph $G=(V,E)$ is a
vertex permutation $\pi: V\to V$ for which $(v,\pi(v))\in E$, for any vertex
$v\in V$. The set of such permutations, denoted by $\Omega(G)$, 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 $\Omega(G)$ 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.
