Addendum to "Tilings problems on Baumslag-Solitar groups"

TL;DR

This paper clarifies and provides a detailed proof that the Domino problem is undecidable for all Baumslag-Solitar groups, building on previous work on weakly aperiodic subshifts.

Contribution

It offers a detailed proof confirming the undecidability of the Domino problem for Baumslag-Solitar groups, extending prior results with clearer arguments.

Findings

Undecidability of the Domino problem for all Baumslag-Solitar groups.

Extension of weakly aperiodic subshift constructions to these groups.

Clarification of the proof methodology from previous work.

Abstract

In our article in MCU'2013 we state the the Domino problem is undecidable for all Baumslag-Solitar groups $BS(m,n)$, and claim that the proof is a direct adaptation of the construction of a weakly aperiodic subshift of finite type for $BS(m,n)$ given in the paper. In this addendum, we clarify this point and give a detailed proof of the undecidability result. We assume the reader is already familiar with the article in MCU'2013.