Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-12-01T04:09:13.793Z Has data issue: false hasContentIssue false
  • English
  • Français

Abelian maximal pattern complexity of words

Published online by Cambridge University Press:  13 August 2013

TETURO KAMAE ,
STEVEN WIDMER  and
LUCA Q. ZAMBONI
TETURO KAMAE
Affiliation:
Advanced Mathematical Institute, Osaka City University, Osaka, 558-8585, Japan email [email protected]
STEVEN WIDMER
Affiliation:
Department of Mathematics, General Academics Building 435, 1155 Union Circle #311430, Denton, TX 76203-5017, USA email [email protected]
LUCA Q. ZAMBONI
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, F69622 Villeurbanne Cedex, France email [email protected] Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland email [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper, we study the maximal pattern complexity of infinite words up to Abelian equivalence. We compute a lower bound for the Abelian maximal pattern complexity of infinite words which are both recurrent and aperiodic by projection. We show that in the case of binary words, the bound is actually achieved and gives a characterization of recurrent aperiodic words.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 1 , February 2015 , pp. 142 - 151
Copyright
© Cambridge University Press, 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Coven, E. M. and Hedlund, G. A.. Sequences with minimal block growth. Math. Syst. Theory 7 (1973), 138–153.CrossRefGoogle Scholar
McCutcheon, R.. Elementary Methods in Ergodic Ramsey Theory (Lecture Notes in Mathematics, 1722). Springer, Berlin, 1999 (in Ch. 2).Google Scholar
Kamae, T. and Zamboni, L. Q.. Sequence entropy and the maximal pattern complexity of infinite words. Ergod. Th. & Dynam. Sys. 22 (2002), 1191–1199.Google Scholar
Kamae, T. and Rao, H.. Maximal pattern complexity over $\ell $ letters. European J. Combin. 27 (2006), 125–137.Google Scholar
Kamae, T.. Uniform sets and super-stationary sets over general alphabets. Ergod. Th. & Dynam. Sys. 31 (2011), 1445–1461.Google Scholar
Morse, M. and Hedlund, G. A.. Symbolic dynamics II: Sturmian trajectories. Amer. J. Math. 62 (1) (1940), 1–42.CrossRefGoogle Scholar
Richomme, G., Saari, K. and Zamboni, L. Q.. Abelian complexity of minimal subshifts. J. Lond. Math. Soc. (2) 83 (2011), 79–95.CrossRefGoogle Scholar