PN sequences obtained from signs of crossings of knot diagrams

Kuniyuki Takaoka

    Research output: Contribution to journalArticle

    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 languageEnglish
    Article number1650058
    JournalJournal of Knot Theory and its Ramifications
    Volume25
    Issue number10
    DOIs
    Publication statusPublished - 2016 Sep 1

    Keywords

    • crossing information
    • Knot diagram
    • negative crossing
    • positive crossing

    ASJC Scopus subject areas

    • Algebra and Number Theory

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