Upper bound on lattice stick number of knots

Kyungpyo Hong; Sungjong No; Seungsang Oh

doi:10.1017/S0305004113000212

Upper bound on lattice stick number of knots

Kyungpyo Hong, Sungjong No, Seungsang Oh

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	173-179
Number of pages	7
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	155
Issue number	1
DOIs	https://doi.org/10.1017/S0305004113000212
Publication status	Published - 2013 Jul

ASJC Scopus subject areas

Mathematics(all)

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abstract = "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.",

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AB - 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.

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Upper bound on lattice stick number of knots

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