Knots with small lattice stick numbers
Geometric Topology
2015-12-14 v1
Abstract
The lattice stick number of a knot type is defined to be the minimal number of straight line segments required to construct a polygon presentation of the knot type in the cubic lattice. In this paper, we mathematically prove that the trefoil knot and the figure-8 knot are the only knot types of lattice stick number less than 15, which verifies the result from previous numerical estimations on this quantity.
Keywords
Cite
@article{arxiv.1512.03582,
title = {Knots with small lattice stick numbers},
author = {Youngsik Huh and Seungsang Oh},
journal= {arXiv preprint arXiv:1512.03582},
year = {2015}
}