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; firstname.lastname@example.org
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
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