RAIRO-Theor. Inf. Appl.
Volume 39, Number 1, January-March 2005Imre Simon, the tropical computer scientist
|Page(s)||207 - 215|
|Published online||15 March 2005|
Episturmian morphisms and a Galois theorem on continued fractions
Present address: 19 rue de Bagneux, 92330 Sceaux, France.
2 LIAFA, ERS 586, Université Paris VII, case 7014, 2 place Jussieu, 75251 Paris Cedex 5, France; email@example.com
We associate with a word w on a finite alphabet A an episturmian (or Arnoux-Rauzy) morphism and a palindrome. We study their relations with the similar ones for the reversal of w. Then when |A|=2 we deduce, using the Sturmian words that are the fixed points of the two morphisms, a proof of a Galois theorem on purely periodic continued fractions whose periods are the reversal of each other.
Mathematics Subject Classification: 11A55 / 68R15
Key words: Episturmian morphism / Arnoux-Rauzy morphism / palindrome / continued fraction / Sturmian word.
© EDP Sciences, 2005
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.