Clock Moves and Alexander Polynomial of Plane Graphs
Geometric Topology
2024-10-23 v2
Abstract
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.
Cite
@article{arxiv.2410.16126,
title = {Clock Moves and Alexander Polynomial of Plane Graphs},
author = {Wenbo Liao and Zhongtao Wu},
journal= {arXiv preprint arXiv:2410.16126},
year = {2024}
}
Comments
29 pages, 27 figures