Toeplitz subshift whose automorphism group is not finitely generated

TL;DR

This paper explicitly characterizes the automorphism group of a specific Toeplitz subshift, revealing it as a non-finitely generated subgroup of rational numbers generated by powers of 5/2, with the shift map corresponding to 1.

Contribution

It provides an explicit representation of the automorphism group for a Toeplitz subshift, demonstrating it is non-finitely generated and generated by powers of 5/2.

Findings

Automorphism group is a non-finitely generated subgroup of rationals.

The shift map corresponds to the rational number 1.

The group is generated by powers of 5/2.

Abstract

We compute an explicit representation of the (topological) automorphism group or a particular Toeplitz subshift. The automorphism group is a (non-finitely generated) subgroup of rational numbers under addition and the shift map corresponds to the rational number 1. The group is the additive subgroup of the rational numbers generated by the powers of 5/2.