TY - JOUR

T1 - Upper bound on lattice stick number of knots

AU - Hong, Kyungpyo

AU - No, Sungjong

AU - Oh, Seungsang

PY - 2013/7

Y1 - 2013/7

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84878807991&partnerID=8YFLogxK

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U2 - 10.1017/S0305004113000212

DO - 10.1017/S0305004113000212

M3 - Article

AN - SCOPUS:84878807991

VL - 155

SP - 173

EP - 179

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

SN - 0305-0041

IS - 1

ER -