Stick numbers of 2-bridge knots and links

Youngsik Huh; Sungjong No; Seungsang Oh

doi:10.1090/S0002-9939-2011-10832-3

Stick numbers of 2-bridge knots and links

Youngsik Huh, Sungjong No, Seungsang Oh

Department of Mathematics

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

10 Citations (Scopus)

Abstract

Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of the minimal crossing number c(K) of the knot, which is s(K) ≤ 2c(K). Furthermore, McCabe proved that s(K) ≤ c(K) + 3 for a 2-bridge knot or link, except in the cases of the unlink and the Hopf link. In this paper we construct any 2-bridge knot or link K of at least six crossings by using only c(K)+2 straight sticks. This gives a new upper bound on stick numbers of 2-bridge knots and links in terms of crossing numbers.

Original language	English
Pages (from-to)	4143-4152
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2011-10832-3
Publication status	Published - 2011 Nov

Keywords

2-bridge
Knot
Stick number

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-2011-10832-3

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AB - Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of the minimal crossing number c(K) of the knot, which is s(K) ≤ 2c(K). Furthermore, McCabe proved that s(K) ≤ c(K) + 3 for a 2-bridge knot or link, except in the cases of the unlink and the Hopf link. In this paper we construct any 2-bridge knot or link K of at least six crossings by using only c(K)+2 straight sticks. This gives a new upper bound on stick numbers of 2-bridge knots and links in terms of crossing numbers.

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KW - Knot

KW - Stick number

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JF - Proceedings of the American Mathematical Society

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Stick numbers of 2-bridge knots and links

Abstract

Keywords

ASJC Scopus subject areas

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