Completing a combinatorial proof of the rigidity of Sturmian words generated by morphisms
type: Item
instance of: scholarly article
title: Completing a combinatorial proof of the rigidity of Sturmian words generated by morphisms
zbMATH Open document ID: 1248.68396
author: Gwénaël Richomme
author: Patrice Séébold
published in: Theoretical Computer Science
publication date: 2012-05-30T00:00:00Z
review text: In [Theor. Comput. Sci. 195, No. 1, 91--109 (1998; Zbl 0981.68104); Lect. Notes Comput. Sci. 1113, 506--516 (1996; Zbl 0889.68094)], the second author proved that Sturmian words generated by morphisms are rigid. There was a gap in the proof; more precisely, in the property that two commuting morphisms \(f\), \(g\) generating the same Sturmian word such that \(f^m= g^n\) for some integers \(n\), \(m\) are necessarily powers of some Sturmian morphism \(h\). This property has to be proved. (The corresponding property for words, known as the Lyndon-Schützenberger theorem, uses the fact that the monoid of words on a finite alphabet is a free monoid.) The authors of the paper under review prove that property, thus filling the gap in the cited papers.
reviewed by: Jean-Paul Allouche
Mathematics Subject Classification ID: 68R15
zbMATH DE Number: 6039155
zbMATH Keywords: Sturmian words
zbMATH Keywords: Sturmian morphisms
zbMATH Keywords: rigidity
MaRDI profile type: Publication
full work available at URL: j.tcs.2011.12.008
OpenAlex ID: W2027342596
cites work: Some remarks about stabilizers
cites work: Syndeticity and independent substitutions
cites work: On stabilizers of infinite words
cites work: Q4529547
cites work: Invertible Substitutions with a Common Periodic Point
cites work: Conjugacy and episturmian morphisms.
cites work: On the conjugation of standard morphisms
DOI: 10.1016/J.TCS.2011.12.008
description: scientific article; zbMATH DE number 6039155