The lattice stick number sL(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 sL(K) ≤ 3c(K) + 2. Moreover if K is a non-alternating prime knot, then sL(K) ≤ 3c(K) - 4.
|Number of pages||7|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 2013 Jul|
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