On Factorially Balanced Sets of Words

Gwenaël Richomme 1, 2 Patrice Séébold 1, 2
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 one 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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Gwenaël Richomme, Patrice Séébold. On Factorially Balanced Sets of Words. [Research Report] RR-10028, Lirmm. 2010. ⟨lirmm-00507782⟩

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