Undecidability of tiling the plane with a fixed number of Wang bars
Combinatorics
2026-01-07 v1 Computational Complexity
Metric Geometry
Abstract
To study the fixed parameter undecidability of tiling problem for a set of Wang tiles, Jeandel and Rolin show that the tiling problem for a set of 44 Wang bars is undecidable. In this paper, we improve their result by proving that whether a set of 29 Wang bars can tile the plane is undecidable. As a consequence, the tiling problem for a set of Wang tiles with color deficiency of 25 is also undecidable.
Cite
@article{arxiv.2404.04504,
title = {Undecidability of tiling the plane with a fixed number of Wang bars},
author = {Chao Yang and Zhujun Zhang},
journal= {arXiv preprint arXiv:2404.04504},
year = {2026}
}