On graph induced symbolic systems

Authors

DOI:

https://doi.org/10.4995/agt.2023.16662

Keywords:

multidimensional shift spaces, shifts of finite type, periodicity in multidimensional shifts of finite type

Abstract

In this paper, we investigate shift spaces arising from a multidimensional graph G. In particular, we investigate nonemptiness and existence of periodic points for a multidimensional shift space. We derive sufficient conditions under which these questions can be answered affirmatively. We investigate the structure of the shift space using the generating matrices. We prove that any d-dimensional shift of finite type is finite if and only if it is conjugate to a shift generated through permutation matrices. We prove that if any triangular pattern of the form a b c can be extended to a 1 x 1 square then the two dimensional shift space possesses periodic points. We introduce the notion of an E-pair for a two dimensional shift space. Using the notion of an E-pair, we derive sufficient conditions for non-emptiness of the two dimensional shift space under discussion.

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Author Biographies

Prashant Kumar, Indian Institute of Technology Jodhpur

Department of Mathematics

Puneet Sharma, Indian Institute of Technology Jodhpur

Department of Mathematics

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Published

2023-10-02

How to Cite

[1]
P. Kumar and P. Sharma, “On graph induced symbolic systems”, Appl. Gen. Topol., vol. 24, no. 2, pp. 359–378, Oct. 2023.

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Section

Regular Articles