Upper bound on lattice stick number of knots

Abstract

The lattice stick number $s_L(K)$ of a knot $K$ is defined to be the minimal number of straight line segments required to construct a stick presentation of $K$ in the cubic lattice. In this paper, we find an upper bound on the lattice stick number of a nontrivial knot $K$, except trefoil knot, in terms of the minimal crossing number $c(K)$ which is $s_L(K)\le 3c(K)+2$. Moreover if $K$ is a non-alternating prime knot, then $s_L(K)\le 3c(K)-4$.

7 pages, 7 figures

References in corpus (3)

• An upper bound on stick numbers of knots
• Stick index of knots and links in the cubic lattice
• Knots with small lattice stick numbers

Cited by in corpus (1)

• Links with small lattice stick numbers