PERMUTATIONS WITH RESTRICTED MOVEMENT

A restricted permutation of a locally finite directed graph G = (V;E) is a vertex permutation pi : V -> V for which (v, pi (v)) is an element of E, for any vertex nu is an element of 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 [18] of restricted 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 Z(d)-permutations. We discuss the global and local admissibility of patterns, in the context of restricted Z(d)-permutations. Finally, we review the related models of injective and surjective restricted functions.