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decimations.

RAIRO - Theoretical Informatics and Applications (1)

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How to build billiard words using decimations
Jean-Pierre Borel
Journal:

RAIRO - Theoretical Informatics and Applications / Volume 44 / Issue 1 / January 2010

Published online by Cambridge University Press:

11 February 2010, pp. 59-77

Print publication:

January 2010
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We present two methods based on decimation for computing finite billiard words on any finite alphabet. The first method computes finite billiard words by iteration of some transformation on words. The number of iterations is explicitly bounded. The second one gives a direct formula for the billiard words. Some results remain true for infinite standard Sturmian words, but cannot be used for computation as they only are limit results.