Decidability, arithmetic subsequences and eigenvalues of morphic subshifts

Fabien Durand (1) , Valérie Goyheneche (2)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée
2 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352

We prove decidability results on the existence of constant subsequences of uniformly recurrent morphic sequences along arithmetic progressions. We use spectral properties of the subshifts they generate to give a first algorithm deciding whether, given p ∈ N, there exists such a constant subsequence along an arithmetic progression of common difference p. In the special case of uniformly recurrent automatic sequences we explicitely describe the sets of such p by means of automata.

Domaines: Systèmes dynamiques [math.DS]; Mathématique discrète [cs.DM]

Fabien Durand, Valérie Goyheneche. Decidability, arithmetic subsequences and eigenvalues of morphic subshifts. Bulletin of the Belgian Mathematical Society - Simon Stevin, 2019, 26 (4), pp.591-618. ⟨10.36045/bbms/1576206359⟩. ⟨hal-01917269v2⟩