Lattice Diagrams of Knots and Diagrams of Lattice Stick Knots

Abstract

We give a simple example showing that a knot or link diagram that lies in the ${\mathbb{Z}}^2$ lattice is not necessarily the projection of a lattice stick knot or link in the ${\mathbb{Z}}^3$ lattice, and we give a necessary and sufficient condition for when a knot or link diagram that lies in the ${\mathbb{Z}}^2$ lattice is in fact the projection of a lattice stick knot or link.

arXiv comment14 figures

References in corpus (1)

• The Ropelengths of Knots Are Almost Linear in Terms of Their Crossing Numbers