{"docId":415,"paperId":415,"url":"https:\/\/dmtcs.episciences.org\/415","doi":"10.46298\/dmtcs.415","journalName":"Discrete Mathematics & Theoretical Computer Science","issn":"","eissn":"1365-8050","volume":[{"vid":82,"name":"Vol. 9 no. 2"}],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-00159681","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-00159681v1","dateSubmitted":"2015-03-26 16:19:45","dateAccepted":"2015-06-09 14:46:44","datePublished":"2007-01-01 08:00:00","titles":{"en":"Infinite special branches in words associated with beta-expansions"},"authors":["Frougny, Christiane","Mas\u00e1kov\u00e1, Zuzana","Pelantov\u00e1, Edita"],"abstracts":{"en":"A Parry number is a real number \u03b2 > 1 such that the R\u00e9nyi \u03b2-expansion of 1 is finite or infinite eventually periodic. If this expansion is finite, \u03b2 is said to be a simple Parry number. Remind that any Pisot number is a Parry number. In a previous work we have determined the complexity of the fixed point u\u03b2 of the canonical substitution associated with \u03b2-expansions, when \u03b2 is a simple Parry number. In this paper we consider the case where \u03b2 is a non-simple Parry number. We determine the structure of infinite left special branches, which are an important tool for the computation of the complexity of u\u03b2. These results allow in particular to obtain the following characterization: the infinite word u\u03b2 is Sturmian if and only if \u03b2 is a quadratic Pisot unit."},"keywords":[["factor complexity function"],["Parry numbers"],"[INFO.INFO-DM] Computer Science [cs]\/Discrete Mathematics [cs.DM]"]}