The clock theorem for knotoids and linkoids
Geometric Topology
2025-09-29 v1 Combinatorics
Abstract
In this paper, we generalize the \textit{Clock Theorem} of Formal Knot Theory to knotoids in . The clock theorem implies that clock states of a knotoid diagram form a lattice under transpositions. These states form the basis of many invariants of knotoids and linkoids including the Alexander polynomial, Mock Alexander polynomial and the Jones polynomial.
Cite
@article{arxiv.2509.21568,
title = {The clock theorem for knotoids and linkoids},
author = {Neslihan Gügümcü and Louis H. Kauffman},
journal= {arXiv preprint arXiv:2509.21568},
year = {2025}
}