## Abstract

A restricted permutation of a locally finite directed graph G = (V, E) is a vertex permutation π : V → V for which (v, π(v)) ∈ E, for any vertex v ∈ V . The set of such permutations, denoted by ?(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 ?(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.

Original language | English |
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Pages (from-to) | 4319-4349 |

Number of pages | 31 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 41 |

Issue number | 9 |

DOIs | |

State | Published - 1 Sep 2021 |

## Keywords

- Dynamical systems
- Perfect matchings
- Planner graphs
- Restricted movement permutations
- Topological entropy

## ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics