How to build billiard words using decimations

Issue		RAIRO-Theor. Inf. Appl. Volume 44, Number 1, January-March 2010 Special issue dedicated to the 12th “Journées Montoises d'Informatique Théorique”


Page(s)		59 - 77
DOI		10.1051/ita/2010005
Published online		11 February 2010

RAIRO-Theor. Inf. Appl. 44 (2010) 59-77

How to build billiard words using decimations

Jean-Pierre Borel

XLim, UMR 6172, Université de Limoges – CNRS, 123 avenue Albert Thomas, 87060 Limoges Cedex, France; borel@unilim.fr

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.

Mathematics Subject Classification: 68R15 / 68Q68

Key words: Decimations.

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