A new approach to the 2-regularity of the -abelian complexity of 2-automatic sequences - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue The Electronic Journal of Combinatorics Année : 2015

A new approach to the 2-regularity of the -abelian complexity of 2-automatic sequences

Résumé

We prove that a sequence satisfying a certain symmetry property is 2-regular in the sense of Allouche and Shallit, i.e., the Z-module generated by its 2-kernel is finitely generated. We apply this theorem to develop a general approach for studying the-abelian complexity of 2-automatic sequences. In particular, we prove that the period-doubling word and the Thue–Morse word have 2-abelian complexity sequences that are 2-regular. Along the way, we also prove that the 2-block codings of these two words have 1-abelian complexity sequences that are 2-regular.
Fichier principal
Vignette du fichier
regular-complexity-arXiv.pdf (424.71 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01144698 , version 1 (22-04-2015)

Identifiants

Citer

Aline Parreau, Michel Rigo, Eric Rowland, Elise Vandomme. A new approach to the 2-regularity of the -abelian complexity of 2-automatic sequences. The Electronic Journal of Combinatorics, 2015, 22 (1), pp.#P1.27. ⟨hal-01144698⟩
144 Consultations
120 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More