Clock Moves and Alexander Polynomial of Plane Graphs
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914982905511936 |
|---|---|
| author | Liao, Wenbo Wu, Zhongtao |
| author_facet | Liao, Wenbo Wu, Zhongtao |
| contents | In this paper, we introduce a notion of clock moves for spanning trees in plane graphs. This enables us to develop a spanning tree model of an Alexander polynomial for a plane graph and prove the unimodal property of its associate coefficient sequence. In particular, this confirms the trapezoidal conjecture for planar singular knots and gives new insights to Fox's original conjecture on alternating knots. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16126 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Clock Moves and Alexander Polynomial of Plane Graphs Liao, Wenbo Wu, Zhongtao Geometric Topology In this paper, we introduce a notion of clock moves for spanning trees in plane graphs. This enables us to develop a spanning tree model of an Alexander polynomial for a plane graph and prove the unimodal property of its associate coefficient sequence. In particular, this confirms the trapezoidal conjecture for planar singular knots and gives new insights to Fox's original conjecture on alternating knots. |
| title | Clock Moves and Alexander Polynomial of Plane Graphs |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2410.16126 |