Lattice stick number of knots**Project supported by the NSFC grants 11531006, 11371367 and 11271290, and the Fundamental Research Funds for the Central Universities 20720160038 and Fujian Province young and middle-aged teacher education research project JA15016.

Abstract

The minimal number of straight line segments required to construct a polygonal presentation of the knot K in the cubic lattice is called the lattice stick number of the knot K, denoted by . It is known that if the crossing number of K, , satisfies , and the main result of this paper is to improve this to if . Furthermore, we will show that for and which implies that this lower bound cannot be improved except for knots with higher crossing numbers.