Finitely Balanced Sequences and Plasticity of 1-Dimensional Tilings

TL;DR

This paper explores how finitely balanced sequences influence the invariance of 1D tiling dynamics under length modifications, showing that such sequences lead to topological conjugacies when tile lengths are changed.

Contribution

It establishes a connection between finitely balanced sequences and the invariance of tiling dynamics under length alterations, highlighting a new property of these sequences.

Findings

Finitely balanced sequences ensure topological conjugacy under tile length changes.

Sequence balancing property relates to tiling invariance.

Length modifications result in conjugate tiling spaces, up to rescaling.

Abstract

We relate a balancing property of letters for bi-infinite sequences to the invariance of the resulting 1-dimensional tiling dynamics under changes in the lengths of the tiles. If the language of the sequence space is finitely balanced, then all length changes in the corresponding tiling space result in topological conjugacies, up to an overall rescaling.