2-Tangle replacements and adequate diagrams

Woo Seok Kim; Jung Hoon Lee; Sam Lee

doi:10.1142/S0218216517500833

2-Tangle replacements and adequate diagrams

Woo Seok Kim
, Jung Hoon Lee^*
, Sam Lee

^*Corresponding author for this work

Department of Mathematics

Jeonbuk National University

Research output: Contribution to journal › Journal article › peer-review

1 Scopus citations

Abstract

We consider 2-tangle replacements of link diagrams, i.e. replacing a crossing of a link diagram D with a 2-tangle diagram T. We show that if D and T are adequate then the 2-tangle replacement, denoted by D_T, is also adequate. This gives a way to obtain infinitely many new minimal crossing diagrams.

Original language	English
Article number	1750083
Journal	Journal of Knot Theory and its Ramifications
Volume	26
Issue number	13
DOIs	https://doi.org/10.1142/S0218216517500833
State	Published - 2017.11.1

Keywords

2-tangle replacement
adequate diagram
Bracket polynomial

Quacquarelli Symonds(QS) Subject Topics

Mathematics

Access to Document

10.1142/S0218216517500833

Cite this

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title = "2-Tangle replacements and adequate diagrams",

abstract = "We consider 2-tangle replacements of link diagrams, i.e. replacing a crossing of a link diagram D with a 2-tangle diagram T. We show that if D and T are adequate then the 2-tangle replacement, denoted by DT, is also adequate. This gives a way to obtain infinitely many new minimal crossing diagrams.",

keywords = "2-tangle replacement, adequate diagram, Bracket polynomial",

author = "Kim, \{Woo Seok\} and Lee, \{Jung Hoon\} and Sam Lee",

note = "Publisher Copyright: {\textcopyright} 2017 World Scientific Publishing Company.",

year = "2017",

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day = "1",

doi = "10.1142/S0218216517500833",

language = "English",

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T1 - 2-Tangle replacements and adequate diagrams

AU - Kim, Woo Seok

AU - Lee, Jung Hoon

AU - Lee, Sam

PY - 2017/11/1

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N2 - We consider 2-tangle replacements of link diagrams, i.e. replacing a crossing of a link diagram D with a 2-tangle diagram T. We show that if D and T are adequate then the 2-tangle replacement, denoted by DT, is also adequate. This gives a way to obtain infinitely many new minimal crossing diagrams.

AB - We consider 2-tangle replacements of link diagrams, i.e. replacing a crossing of a link diagram D with a 2-tangle diagram T. We show that if D and T are adequate then the 2-tangle replacement, denoted by DT, is also adequate. This gives a way to obtain infinitely many new minimal crossing diagrams.

KW - 2-tangle replacement

KW - adequate diagram

KW - Bracket polynomial

UR - https://www.scopus.com/pages/publications/85030834639

U2 - 10.1142/S0218216517500833

DO - 10.1142/S0218216517500833

M3 - Journal article

AN - SCOPUS:85030834639

SN - 0218-2165

VL - 26

JO - Journal of Knot Theory and its Ramifications

JF - Journal of Knot Theory and its Ramifications

IS - 13

M1 - 1750083

ER -

2-Tangle replacements and adequate diagrams

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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