Lattice stick numbers of small knots

Youngsik Huh; Seungsang Oh

doi:10.1142/S0218216505004160

Lattice stick numbers of small knots

Youngsik Huh, Seungsang Oh

Department of Mathematics

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

19 Citations (Scopus)

Abstract

Lattice stick number s_L (K) is defined to be the minimal number of sticks required to construct a polygonal representation of the knot K in the cubic lattice. In this paper, we give lattice stick numbers of small knots such as 3₁ and 4₁. More precisely we prove that s _L(3₁) = 12 and s_L(K) ≥ 14 for any other non-trivial knot K.

Original language	English
Pages (from-to)	859-867
Number of pages	9
Journal	Journal of Knot Theory and its Ramifications
Volume	14
Issue number	7
DOIs	https://doi.org/10.1142/S0218216505004160
Publication status	Published - 2005 Nov

Keywords

Cubic lattice
Knot
Stick number

ASJC Scopus subject areas

Algebra and Number Theory

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title = "Lattice stick numbers of small knots",

abstract = "Lattice stick number sL (K) is defined to be the minimal number of sticks required to construct a polygonal representation of the knot K in the cubic lattice. In this paper, we give lattice stick numbers of small knots such as 31 and 41. More precisely we prove that s L(31) = 12 and sL(K) ≥ 14 for any other non-trivial knot K.",

keywords = "Cubic lattice, Knot, Stick number",

author = "Youngsik Huh and Seungsang Oh",

note = "Funding Information: The first author was supported by the research fund of Hanyang University (HY-2004). The second author (corresponding author) was supported by a Korea University Grant.",

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AU - Oh, Seungsang

N1 - Funding Information: The first author was supported by the research fund of Hanyang University (HY-2004). The second author (corresponding author) was supported by a Korea University Grant.

PY - 2005/11

Y1 - 2005/11

N2 - Lattice stick number sL (K) is defined to be the minimal number of sticks required to construct a polygonal representation of the knot K in the cubic lattice. In this paper, we give lattice stick numbers of small knots such as 31 and 41. More precisely we prove that s L(31) = 12 and sL(K) ≥ 14 for any other non-trivial knot K.

AB - Lattice stick number sL (K) is defined to be the minimal number of sticks required to construct a polygonal representation of the knot K in the cubic lattice. In this paper, we give lattice stick numbers of small knots such as 31 and 41. More precisely we prove that s L(31) = 12 and sL(K) ≥ 14 for any other non-trivial knot K.

KW - Cubic lattice

KW - Knot

KW - Stick number

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U2 - 10.1142/S0218216505004160

DO - 10.1142/S0218216505004160

M3 - Article

AN - SCOPUS:27844539026

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JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

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ER -

Lattice stick numbers of small knots

Abstract

Keywords

ASJC Scopus subject areas

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