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September 2021 A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings
Ayşe A. Şahin, Michael Schraudner, Ilie Ugarcovici
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Illinois J. Math. 65(3): 655-686 (September 2021). DOI: 10.1215/00192082-9446050

Abstract

We explicitly construct a strongly aperiodic subshift of finite type for the discrete Heisenberg group. Our example builds on the classical aperiodic tilings of the plane due to Raphael Robinson. Extending those tilings to the Heisenberg group by exploiting the group’s structure and posing additional local rules to prune out remaining periodic behavior, we maintain a rich projective subdynamics on Z2 cosets. In addition, the obtained subshift factors onto a strongly aperiodic, minimal sofic shift via a map that is invertible on a dense set of configurations.

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Ayşe A. Şahin. Michael Schraudner. Ilie Ugarcovici. "A strongly aperiodic shift of finite type on the discrete Heisenberg group using Robinson tilings." Illinois J. Math. 65 (3) 655 - 686, September 2021. https://doi.org/10.1215/00192082-9446050

Information

Received: 8 December 2020; Revised: 15 July 2021; Published: September 2021
First available in Project Euclid: 31 August 2021

Digital Object Identifier: 10.1215/00192082-9446050

Subjects:
Primary: 37B10
Secondary: 37B50

Rights: Copyright © 2021 by the University of Illinois at Urbana–Champaign

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Vol.65 • No. 3 • September 2021
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