Digital lines, Sturmian words, and continued fractions
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چکیده
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منابع مشابه
Words and fractions
This article presents some results about Sturmian words and continued fractions — none of them new — which are needed in my not yet written paper about regular expressions. I have tried to find as direct a route as possible to the important results starting from first principles. The style is somewhat terse, and the reader (if reader there be) will find it useful to work out examples of the def...
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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. Ma...
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In this survey paper, we present some recent results concerning nite and innnite Stur-mian words. We emphasize on the diierent deenitions of Sturmian words, and various subclasses, and give the ways to construct them related to continued fraction expansion. Next, we give properties of special nite Sturmian words, called standard words. Among these, a decomposition into palindromes, a relation w...
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We present a new, dynamical way to study powers (or repetitions) in Sturmian words based on results from Diophantine approximation theory. As a result, we provide an alternative and shorter proof of a result by Damanik and Lenz characterizing powers in Sturmian words [Powers in Sturmian Sequences, European J. Combin. 24 (2003), 377–390]. Further, as a consequence, we obtain a previously known f...
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We introduce a new geometric approach to Sturmian words by means of a mapping that associates certain lines in the n× n-grid and sets of finite Sturmian words of length n. Using this mapping, we give new proofs of the formulas enumerating the finite Sturmian words and the palindromic finite Sturmian words of a given length. We also give a new proof for the well-known result that a factor of a S...
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