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Journal Articles Theoretical Computer Science Year : 2011

On Factorially Balanced Sets of Words

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.

Dates and versions

lirmm-00616826 , version 1 (24-08-2011)

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Cite

Gwenaël Richomme, Patrice Séébold. On Factorially Balanced Sets of Words. Theoretical Computer Science, 2011, 412 (39), pp.5492-5497. ⟨10.1016/j.tcs.2011.06.027⟩. ⟨lirmm-00616826⟩

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