## Abstract

Let (Formula presented.) be a convex polygon with each vertex in it labeled by an element from a finite set and such that the labeling of each vertex (Formula presented.) is uniquely determined by the labeling of all other points in the polygon. We introduce a class of (Formula presented.) -shift systems, the polygonal shifts, determined by such a polygon: These are shift systems such that the restriction of any (Formula presented.) to some polygon (Formula presented.) has this property. These polygonal systems are related to various well-studied classes of shift systems, including subshifts of finite type and algebraic shifts, but also many other systems. We give necessary conditions for a (Formula presented.) -system (Formula presented.) to be polygonal, in terms of the nonexpansive subspaces of (Formula presented.), and under further conditions can give a complete characterization for such systems.

Original language | English (US) |
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Pages (from-to) | 252-286 |

Number of pages | 35 |

Journal | Proceedings of the London Mathematical Society |

Volume | 121 |

Issue number | 2 |

DOIs | |

State | Published - Aug 1 2020 |

## Keywords

- 37B10
- 37B15
- 37B40
- 37B50 (primary)

## ASJC Scopus subject areas

- Mathematics(all)