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Article Dans Une Revue European Journal of Combinatorics Année : 2016

Abelian bordered factors and periodicity

Résumé

A finite word is u is said to be bordered if u has a proper prefix which is also a suffix of u, and unbordered otherwise. Ehrenfeucht and Silberger proved that an infinite word is purely periodic if and only if it contains only finitely many unbordered factors. We are interested in abelian and weak abelian analogues of this result; namely, we investigate the following question(s): Let w be an infinite word such that all sufficiently long factors are (weakly) abelian bordered; is w (weakly) abelian periodic? In the process we answer a question of Avgustinovich et al. concerning the abelian critical factorization theorem.
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Dates et versions

hal-01829169 , version 1 (03-07-2018)

Identifiants

  • HAL Id : hal-01829169 , version 1

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Emilie Charlier, Tero Harju, Svetlana Puzynina, Luca Q. Zamboni. Abelian bordered factors and periodicity. European Journal of Combinatorics, 2016, 51, pp.407--418. ⟨hal-01829169⟩
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