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On Factorially Balanced Sets of Words

Gwenaël Richomme 1, 2 Patrice Séébold 2, 1
1 ARITH - Arithmétique informatique
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : A set of words is factorially balanced if the set of all the factors of its words is balanced. We prove that if all words of a factorially balanced set have a finite index, then this set is a subset of the set of factors of a Sturmian word. Moreover, characterizing the set of factors of a given length n of a Sturmian word by the left special factor of length n−1 of this Sturmian word, we provide an enumeration formula for the number of sets of words that correspond to some set of factors of length n of a Sturmian word.
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Contributor : Gwenaël Richomme <>
Submitted on : Wednesday, August 24, 2011 - 3:15:25 PM
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Gwenaël Richomme, Patrice Séébold. On Factorially Balanced Sets of Words. Theoretical Computer Science, Elsevier, 2011, 412 (39), pp.5492-5497. ⟨10.1016/j.tcs.2011.06.027⟩. ⟨lirmm-00616826⟩



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