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 the trefoil knot, in terms of the minimal crossing number c(K) which is s(L)(K) <= 3c(K) + 2. Moreover if K is a non-alternating prime knot, then s(L)(K) <= 3c(K) - 4.