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Embedding subshifts of finite type into the Fibonacci–Dyck shift

Published online by Cambridge University Press:  12 May 2016

TOSHIHIRO HAMACHI  and
WOLFGANG KRIEGER
TOSHIHIRO HAMACHI
Affiliation:
Faculty of Mathematics, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan email hamachi@math.kyushu-u.ac.jp
WOLFGANG KRIEGER
Affiliation:
Institute for Applied Mathematics, University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany email krieger@math.uni-heidelberg.de
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Abstract

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A necessary and sufficient condition is given for the existence of an embedding of an irreducible subshift of finite type into the Fibonacci–Dyck shift.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 6 , September 2017 , pp. 1862 - 1886
Copyright
© Cambridge University Press, 2016 

References

Berstel, J. and Perrin, D.. The origins of combinatorics on words. European J. Combin. 28 (2007), 996–1022.Google Scholar
Berstel, J., Perrin, D. and Reutenauer, Ch.. Codes and Automata. Cambridge University Press, Cambridge, 2010.Google Scholar
Hamachi, T. and Inoue, K.. Embeddings of shifts of finite type into the Dyck shift. Monatsh. Math. 145 (2005), 107–129.Google Scholar
Hamachi, T., Inoue, K. and Krieger, W.. Subsystems of finite type and semigroup invariants of subshifts. J. Reine Angew. Math. 632 (2009), 37–61.Google Scholar
Hamachi, T. and Krieger, W.. A construction of subshifts and a class of semigroups. Preprint, 2013, arXiv:1303.4158 [math.DS].Google Scholar
Kitchens, B. P.. Symbolic Dynamics. Springer, New York, 1998.Google Scholar
Krieger, W. and Matsumoto, K.. Zeta functions and topological entropy of the Markov–Dyck shifts. Münster J. Math. 4 (2011), 171–184.Google Scholar
Krieger, W.. On the uniqueness of the equilibrium state. Math. Syst. Theory 8 (1974), 97–104.Google Scholar
Krieger, W.. On a syntactically defined invariant of symbolic dynamics. Ergod. Th. & Dynam. Sys. 20 (2000), 501–516.Google Scholar
Lind, D. and Marcus, B.. An Introduction to Symbolic Dynamics and Coding. Cambridge University Press, Cambridge, 1995.Google Scholar
Matsumoto, K.. C ∗ -algebras arising from Dyck systems of topological Markov chains. Math. Scand. 109 (2011), 31–54.CrossRefGoogle Scholar
Nivat, M. and Perrot, J.-F.. Une généralisation du monoîde bicyclique. C. R. Math. Acad. Sci. Paris 271 (1970), 824–827.Google Scholar
Perrin, D.. Algebraic combinatorics on words. Algebraic Combinatorics and Computer Science. Eds. Crapo, H. and Senato, D.. Springer, Berlin, Heidelberg, New York, 2001, pp. 391–430.Google Scholar