Knots with small lattice stick numbers

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 $3_1$ and the figure-8 knot $4_1$ are the only knot types of lattice stick number less than 15, which verifies the result from previous numerical estimations on this quantity.

Cited by in corpus (4)

• Stick index of knots and links in the cubic lattice
• Upper bound on lattice stick number of knots
• Bounds in simple hexagonal lattice and classification of 11-stick knots
• The stick number of rail arcs