English

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 313_1 and the figure-8 knot 414_1 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}
}
R2 v1 2026-06-22T12:07:10.151Z