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.
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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 -