Generalised Kauffman Clock Theorems
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866918153753198592 |
|---|---|
| author | Le, Nguyen Thanh Tung Mathews, Daniel V. |
| author_facet | Le, Nguyen Thanh Tung Mathews, Daniel V. |
| contents | Kauffman's clock theorem provides a distributive lattice structure on the set of states of a four-valent graph in the plane. We prove two distinct generalisations of this theorem, for four-valent graphs embedded in more general compact oriented surfaces. The proofs use results of Propp providing distributive lattice structures on matchings on bipartite plane graphs, and orientations of graphs with fixed circulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_02911 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalised Kauffman Clock Theorems Le, Nguyen Thanh Tung Mathews, Daniel V. Geometric Topology Combinatorics 57M15 (Primary) 57K12, 06D99, 05C10 (Secondary) Kauffman's clock theorem provides a distributive lattice structure on the set of states of a four-valent graph in the plane. We prove two distinct generalisations of this theorem, for four-valent graphs embedded in more general compact oriented surfaces. The proofs use results of Propp providing distributive lattice structures on matchings on bipartite plane graphs, and orientations of graphs with fixed circulation. |
| title | Generalised Kauffman Clock Theorems |
| topic | Geometric Topology Combinatorics 57M15 (Primary) 57K12, 06D99, 05C10 (Secondary) |
| url | https://arxiv.org/abs/2510.02911 |