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Reports (Research Report) Year : 2010

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 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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Dates and versions

lirmm-00507782 , version 1 (31-07-2010)

Identifiers

  • HAL Id : lirmm-00507782 , version 1

Cite

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