A construction of the hat tilings by a Markov partition
Combinatorics
2026-04-24 v1 Dynamical Systems
Metric Geometry
Abstract
We present a simple construction of hat tilings. The construction can be carried out by superimposing a triangular grid on a specially colored image and reading off the orientation of the tiles. We show that our construction produces valid hat tilings, and conversely, in an appropriate sense that is made precise in the paper, that every valid hat tiling can be obtained in this way.
Keywords
Cite
@article{arxiv.2604.20964,
title = {A construction of the hat tilings by a Markov partition},
author = {Sébastien Labbé and Peter Selinger},
journal= {arXiv preprint arXiv:2604.20964},
year = {2026}
}
Comments
16 pages, 12 figures