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How to build billiard wordsusing decimations

Published online by Cambridge University Press:  11 February 2010

Jean-Pierre Borel
Jean-Pierre Borel*
Affiliation:
XLim, UMR 6172, Université de Limoges – CNRS, 123 avenue Albert Thomas, 87060 Limoges Cedex, France; borel@unilim.fr
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Abstract

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.

Keywords

Decimations.

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