English

Snakes can be fooled into thinking they live in a tree

Group Theory 2024-09-24 v1 Logic in Computer Science Dynamical Systems Logic

Abstract

We construct a finitely generated group which is not virtually free, yet has decidable snake tiling problem. This shows that either a long-standing conjecture by Ballier and Stein (the characterization of groups with decidable domino problem as those virtually free ones) is false, or a question by Aubrun and Bitar has a positive answer (there exists a group for which the domino and snake problems are of different difficulty).

Cite

@article{arxiv.2409.14525,
  title  = {Snakes can be fooled into thinking they live in a tree},
  author = {Laurent Bartholdi and Ville Salo},
  journal= {arXiv preprint arXiv:2409.14525},
  year   = {2024}
}
R2 v1 2026-06-28T18:52:59.977Z