PN sequences obtained from signs of crossings of knot diagrams

Kuniyuki Takaoka

doi:10.1142/S0218216516500589

PN sequences obtained from signs of crossings of knot diagrams

Kuniyuki Takaoka^*

^*Corresponding author for this work

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

Abstract

For an oriented knot diagram, we define a cyclic word in letters P and N corresponding to positive and negative crossings along the diagram, respectively. We give a necessary and sufficient condition for a cyclic word in P and N to be obtained from some knot diagram. Also, we prove that any PN sequence of a diagram of a nontrivial knot contains at least four subsequences PP and NN.

Original language	English
Article number	1650058
Journal	Journal of Knot Theory and its Ramifications
Volume	25
Issue number	10
DOIs	https://doi.org/10.1142/S0218216516500589
Publication status	Published - 2016 Sept 1

Keywords

crossing information
Knot diagram
negative crossing
positive crossing

ASJC Scopus subject areas

Algebra and Number Theory

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10.1142/S0218216516500589

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abstract = "For an oriented knot diagram, we define a cyclic word in letters P and N corresponding to positive and negative crossings along the diagram, respectively. We give a necessary and sufficient condition for a cyclic word in P and N to be obtained from some knot diagram. Also, we prove that any PN sequence of a diagram of a nontrivial knot contains at least four subsequences PP and NN.",

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AB - For an oriented knot diagram, we define a cyclic word in letters P and N corresponding to positive and negative crossings along the diagram, respectively. We give a necessary and sufficient condition for a cyclic word in P and N to be obtained from some knot diagram. Also, we prove that any PN sequence of a diagram of a nontrivial knot contains at least four subsequences PP and NN.

KW - crossing information

KW - Knot diagram

KW - negative crossing

KW - positive crossing

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JF - Journal of Knot Theory and its Ramifications

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ER -

PN sequences obtained from signs of crossings of knot diagrams

Abstract

Keywords

ASJC Scopus subject areas

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