$S$-adic conjecture and Bratteli diagrams

TL;DR

This paper improves a key result on $S$-adic subshifts and demonstrates how to represent them using Bratteli-Vershik diagrams, enhancing understanding of their structure.

Contribution

It provides a significant enhancement of Ferenczi's result and introduces Bratteli-Vershik representations for $S$-adic subshifts.

Findings

Improved the result of Ferenczi on $S$-adic subshifts

Established Bratteli-Vershik representations for these subshifts

Enhanced structural understanding of $S$-adic systems

Abstract

In this note we apply a substantial improvement of a result of S. Ferenczi on $S$-adic subshifts to give Bratteli-Vershik representations of these subshifts.