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

6 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)

Access to Document

10.1017/S0305004113000212

Fingerprint Dive into the research topics of 'Upper bound on lattice stick number of knots'. Together they form a unique fingerprint.

Cite this

@article{b635c1eef77c4ef59de88f49dc5f40f7,

title = "Upper bound on lattice stick number of knots",

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.",

author = "Kyungpyo Hong and Sungjong No and Seungsang Oh",

year = "2013",

month = jul,

doi = "10.1017/S0305004113000212",

language = "English",

volume = "155",

pages = "173--179",

journal = "Mathematical Proceedings of the Cambridge Philosophical Society",

issn = "0305-0041",

publisher = "Cambridge University Press",

number = "1",

}

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

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

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 -