Sturmian morphisms and α-words

✍ Scribed by Chuan Wai-Fong

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 902 KB
• Volume: 225
• Category: Article
• ISSN: 0304-3975
• DOI: 10.1016/s0304-3975(97)00239-9

✦ Synopsis

In this paper we prove that the set W" of cc-words over (0, I} coincides with the set of images of 0 under Sturmian morphisms. This gives an alternative approach of generating z-words. For each w E W, a Sturmian solution H of the equation w = H(0) which is a composition of Sturmian morphisms of special forms can be constructed explicitly. In order to demonstrate how results on Sturmian morphic images are reformulated as results on r-words and vice versa, we give a Sturmian proof for the conjugation and reversion theorem of a-words obtained by the present author in an earlier paper.