Nous donnons une représentation géométrique des suites doubles uniformément récurrentes de fonction de complexité rectangulaire . Nous montrons que ces suites codent l’action d’une -action définie par deux rotations irrationnelles sur le cercle unité. La preuve repose sur une étude des suites doubles dont les lignes sont des suite sturmiennes de même langage.
For polyominoes coded by their boundary word, we describe a quadratic algorithm in the boundary length which improves the naive algorithm. Techniques used emanate from algorithmics, discrete geometry and combinatorics on words.
Considering each occurrence of a word in a recurrent infinite word, we define the set of return words of to be the set of all distinct words beginning with an occurrence of and ending exactly just before the next occurrence of in the infinite word. We give a simpler proof of the recent result (of the second author) that an infinite word is Sturmian if and only if each of its factors has exactly two return words in it. Then, considering episturmian infinite words, which are a natural generalization...
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