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Permutations with restricted movement
- Publication Year :
- 2020
-
Abstract
- 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.<br />Comment: To be published in Discrete and Continuous Dynamical Systems Journal
- Subjects :
- Vertex (graph theory)
Mathematics::Combinatorics
Group (mathematics)
Computer Science::Information Retrieval
Applied Mathematics
Order (ring theory)
Context (language use)
Dynamical Systems (math.DS)
Subshift of finite type
Injective function
Surjective function
Combinatorics
Permutation
FOS: Mathematics
Discrete Mathematics and Combinatorics
Mathematics - Combinatorics
Combinatorics (math.CO)
Mathematics - Dynamical Systems
Analysis
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....261b895e013d00aaab771f581a670a0e