Upper bound on lattice stick number of knots

KyungPyo Hong; SungJong No; SeungSang Oh

doi:10.1017/s0305004113000212

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arXiv · 1209.0048

Upper bound on lattice stick number of knots

KyungPyo Hong·SungJong No·SeungSang Oh

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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 $s_L(K) \leq 3 c(K) +2$. Moreover if $K$ is a non-alternating prime knot, then $s_L(K) \leq 3 c(K) - 4$.

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BibTeX RIS

KyungPyo Hong, SungJong No, SeungSang Oh. 2012-09-01. Upper bound on lattice stick number of knots. https://doi.org/10.1017/s0305004113000212

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