Slopes of 3-dimensional Subshifts of Finite Type

Etienne Moutot (1, 2) , Pascal Vanier (3)

1 MC2 - Modèles de calcul, Complexité, Combinatoire
2 Department of Mathematics and Statistics, University of Turku
3 LACL - Laboratoire d'Algorithmique Complexité et Logique

In this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope being the angles of the periodicity vector. In this paper, we prove that any Σ_2 set may be realized as a a set of slopes of an SFT.

Domaines: Mathématique discrète [cs.DM]; Informatique [cs]

Etienne Moutot, Pascal Vanier. Slopes of 3-dimensional Subshifts of Finite Type. CSR 2018, Jun 2018, Moscou, Russia. pp.257--268, ⟨10.1007/978-3-319-90530-3_22⟩. ⟨hal-01772574⟩