An upper bound of arc index of links

Yongju Bae; Chan Young Park

doi:10.1017/S0305004100004576

An upper bound of arc index of links

Yongju Bae, Chan Young Park

Kyungpook National University

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

40 Scopus citations

Abstract

In 1996, Cromwell and Nutt [7] found an upper bound on the arc index which is related to the minimal crossing number and conjectured that the upper bound achieves the lowest possible index for alternating links. CONJECTURE. Let L be any prime link. Then α(L) ≤ c(L)+2. Moreover this inequality is strict if and only if L is not alternating. In this paper, we define a new diagram, called a wheel diagram, of a link and use it to prove this conjecture.

Original language	English
Pages (from-to)	491-500
Number of pages	10
Journal	Mathematical Proceedings of the Cambridge Philosophical Society
Volume	129
Issue number	3
DOIs	https://doi.org/10.1017/S0305004100004576
State	Published - Nov 2000

Access to Document

10.1017/S0305004100004576

Cite this

@article{622db0974a3b465caf0468bd456ec582,

title = "An upper bound of arc index of links",

abstract = "In 1996, Cromwell and Nutt [7] found an upper bound on the arc index which is related to the minimal crossing number and conjectured that the upper bound achieves the lowest possible index for alternating links. CONJECTURE. Let L be any prime link. Then α(L) ≤ c(L)+2. Moreover this inequality is strict if and only if L is not alternating. In this paper, we define a new diagram, called a wheel diagram, of a link and use it to prove this conjecture.",

author = "Yongju Bae and Park, {Chan Young}",

year = "2000",

month = nov,

doi = "10.1017/S0305004100004576",

language = "English",

volume = "129",

pages = "491--500",

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

issn = "0305-0041",

publisher = "Cambridge University Press",

number = "3",

}

TY - JOUR

T1 - An upper bound of arc index of links

AU - Bae, Yongju

AU - Park, Chan Young

PY - 2000/11

Y1 - 2000/11

N2 - In 1996, Cromwell and Nutt [7] found an upper bound on the arc index which is related to the minimal crossing number and conjectured that the upper bound achieves the lowest possible index for alternating links. CONJECTURE. Let L be any prime link. Then α(L) ≤ c(L)+2. Moreover this inequality is strict if and only if L is not alternating. In this paper, we define a new diagram, called a wheel diagram, of a link and use it to prove this conjecture.

AB - In 1996, Cromwell and Nutt [7] found an upper bound on the arc index which is related to the minimal crossing number and conjectured that the upper bound achieves the lowest possible index for alternating links. CONJECTURE. Let L be any prime link. Then α(L) ≤ c(L)+2. Moreover this inequality is strict if and only if L is not alternating. In this paper, we define a new diagram, called a wheel diagram, of a link and use it to prove this conjecture.

UR - http://www.scopus.com/inward/record.url?scp=33746827390&partnerID=8YFLogxK

U2 - 10.1017/S0305004100004576

DO - 10.1017/S0305004100004576

M3 - Article

AN - SCOPUS:33746827390

SN - 0305-0041

VL - 129

SP - 491

EP - 500

JO - Mathematical Proceedings of the Cambridge Philosophical Society

JF - Mathematical Proceedings of the Cambridge Philosophical Society

IS - 3

ER -

An upper bound of arc index of links

Abstract

Access to Document

Other files and links

Fingerprint

Cite this