Infinite Schnyder Woods
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917071596552192 |
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| author | Addario-Berry, Louigi Hogan, Emma Michel, Lukas Scott, Alex |
| author_facet | Addario-Berry, Louigi Hogan, Emma Michel, Lukas Scott, Alex |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_07601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinite Schnyder Woods Addario-Berry, Louigi Hogan, Emma Michel, Lukas Scott, Alex Combinatorics Discrete Mathematics Probability 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. |
| title | Infinite Schnyder Woods |
| topic | Combinatorics Discrete Mathematics Probability |
| url | https://arxiv.org/abs/2511.07601 |