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. (24th November 2017) - Huang, Yuanfei
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 S L ( K ) . It is known that S L ( K ) ⩾ 15 if the crossing number of K, C r ( K ), satisfies C r ( K ) ⩾ 5, and the main result of this paper is to improve this to S L ( K ) ⩾ 16 if C r ( K ) ⩾ 5 . Furthermore, we will show that S L ( K ) = 16 for K = 5 1 and K = 5 2 which implies that this lower bound cannot be improved except for knots with higher crossing numbers.