Periodic codings of Bratteli-Vershik systems

TL;DR

This paper establishes conditions under which Bratteli-Vershik systems can be represented by periodic symbolic codings, aiding the understanding of their subshift representations on finite alphabets.

Contribution

It introduces new criteria for when a Bratteli-Vershik system's coding is periodic, linking it to symbolic recursive schemes and cutting-stacking processes.

Findings

Conditions for periodic coding of Bratteli-Vershik systems

Connection between initial path segments and symbolic recursions

Advancement in representing systems as finite alphabet subshifts

Abstract

We develop conditions for the coding of a Bratteli-Vershik system according to initial path segments to be periodic, equivalently for a constructive symbolic recursive scheme corresponding to a cutting and stacking process to produce a periodic sequence. This is a step toward understanding when a Bratteli-Vershik system can be essentially faithfully represented by means of a natural coding as a subshift on a finite alphabet.