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On the Perron root and eigenvectors associated with a subshift of finite type
- Publication Year :
- 2020
-
Abstract
- In this paper, we describe the relationship between the Perron root and eigenvectors of an irreducible subshift of finite type with the correlation between the forbidden words in the subshift. In particular, we derive an expression for the Perron eigenvectors of the associated adjacency matrix. As an application, we obtain the Perron eigenvectors for irreducible $(0,1)$ matrices which are adjacency matrices for directed graphs. Moreover, we derive an alternate definition of the Parry measure in ergodic theory on an irreducible subshift of finite type.<br />Python code added
- Subjects :
- Numerical Analysis
Pure mathematics
Algebra and Number Theory
Mathematics::Dynamical Systems
Root (chord)
Directed graph
Dynamical Systems (math.DS)
Expression (computer science)
Subshift of finite type
Measure (mathematics)
FOS: Mathematics
Discrete Mathematics and Combinatorics
Ergodic theory
Mathematics - Combinatorics
Geometry and Topology
Adjacency matrix
Combinatorics (math.CO)
Mathematics - Dynamical Systems
Eigenvalues and eigenvectors
Computer Science::Formal Languages and Automata Theory
Mathematics
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....c9b4a91d91422fe7466e57b0e3226707