Infinite Schnyder Woods
Combinatorics
2025-11-12 v1 Discrete Mathematics
Probability
Abstract
It is well-known that any finite triangulation possesses a unique maximal Schnyder wood. We introduce Schnyder woods of infinite triangulations, and prove there exists a unique maximal Schnyder wood of any infinite triangulation with finite boundary, and of the uniform infinite half-planar triangulation. Furthermore, the maximal Schnyder wood of the uniform infinite planar triangulation is the limit of maximal Schnyder woods of large finite random triangulations. Several structural properties of infinite Schnyder woods are also described.
Cite
@article{arxiv.2511.07601,
title = {Infinite Schnyder Woods},
author = {Louigi Addario-Berry and Emma Hogan and Lukas Michel and Alex Scott},
journal= {arXiv preprint arXiv:2511.07601},
year = {2025}
}
Comments
68 pages, 15 figures