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Conference Papers Year : 2018

Slopes of 3-dimensional Subshifts of Finite Type

Etienne Moutot
Modèles de calcul, Complexité, Combinatoire
University of Turku
Pascal Vanier
Laboratoire d'Algorithmique Complexité et Logique
CV

Abstract

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.

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Discrete Mathematics [cs.DM] Computer Science [cs]
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https://hal.science/hal-01772574

Submitted on : Friday, April 20, 2018-1:53:13 PM

Last modification on : Thursday, July 18, 2024-5:00:15 PM

Long-term archiving on: Tuesday, September 18, 2018-9:08:00 PM

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hal-01772574 , version 1 (20-04-2018)

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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⟩

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