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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 kamae@apost.plala.or.jp
STEVEN WIDMER
Affiliation:
Department of Mathematics, General Academics Building 435, 1155 Union Circle #311430, Denton, TX 76203-5017, USA email s.widmer1@gmail.com
LUCA Q. ZAMBONI
Affiliation:
Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, F69622 Villeurbanne Cedex, France email lupastis@gmail.com Department of Mathematics and Turku Centre for Computer Science, University of Turku, 20014 Turku, Finland email lupastis@gmail.com
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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 

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