An upper bound on stick number of knots

Youngsik Huh; Seungsang Oh

doi:10.1142/S0218216511008966

An upper bound on stick number of knots

Youngsik Huh, Seungsang Oh

Department of Mathematics

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

14 Citations (Scopus)

Abstract

In 1991, Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of crossing number c(K) which is s(K) ≤ 2c(K). In this paper we give a new upper bound in terms of arc index, and improve Negami's upper bound to s(K) ≤ 3/2 (c(K)+1). Moreover if K is a nonalternating prime knot, then s(K) ≤ 3/2 c(K).

Original language	English
Pages (from-to)	741-747
Number of pages	7
Journal	Journal of Knot Theory and its Ramifications
Volume	20
Issue number	5
DOIs	https://doi.org/10.1142/S0218216511008966
Publication status	Published - 2011 May

Keywords

Knot
stick number
upper bound

ASJC Scopus subject areas

Algebra and Number Theory

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abstract = "In 1991, Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of crossing number c(K) which is s(K) ≤ 2c(K). In this paper we give a new upper bound in terms of arc index, and improve Negami's upper bound to s(K) ≤ 3/2 (c(K)+1). Moreover if K is a nonalternating prime knot, then s(K) ≤ 3/2 c(K).",

keywords = "Knot, stick number, upper bound",

author = "Youngsik Huh and Seungsang Oh",

note = "Funding Information: This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. R01-2007-000-20293-0). The second author was supported by a Korea University Grant.",

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AU - Huh, Youngsik

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N1 - Funding Information: This work was supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. R01-2007-000-20293-0). The second author was supported by a Korea University Grant.

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N2 - In 1991, Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of crossing number c(K) which is s(K) ≤ 2c(K). In this paper we give a new upper bound in terms of arc index, and improve Negami's upper bound to s(K) ≤ 3/2 (c(K)+1). Moreover if K is a nonalternating prime knot, then s(K) ≤ 3/2 c(K).

AB - In 1991, Negami found an upper bound on the stick number s(K) of a nontrivial knot K in terms of crossing number c(K) which is s(K) ≤ 2c(K). In this paper we give a new upper bound in terms of arc index, and improve Negami's upper bound to s(K) ≤ 3/2 (c(K)+1). Moreover if K is a nonalternating prime knot, then s(K) ≤ 3/2 c(K).

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ER -

An upper bound on stick number of knots

Abstract

Keywords

ASJC Scopus subject areas

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