Unknotting numbers of diagrams of a given nontrivial knot are unbounded

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    We show that for any nontrivial knot K and any natural number n, there is a diagram D of K such that the unknotting number of D is greater than or equal to n. It is well-known that twice the unknotting number of K is less than or equal to the crossing number of K minus one. We show that the equality holds only when K is a (2, p)-torus knot.

    Original languageEnglish
    Pages (from-to)1049-1063
    Number of pages15
    JournalJournal of Knot Theory and its Ramifications
    Volume18
    Issue number8
    DOIs
    Publication statusPublished - 2009 Aug

    Fingerprint

    Unknotting number
    Knot
    Diagram
    Torus knot
    Crossing number
    Less than or equal to
    Natural number
    Equality

    Keywords

    • Crossing number.
    • Knot
    • Unknotting number
    • Unknotting number of diagram

    ASJC Scopus subject areas

    • Algebra and Number Theory

    Cite this

    Unknotting numbers of diagrams of a given nontrivial knot are unbounded. / Taniyama, Kouki.

    In: Journal of Knot Theory and its Ramifications, Vol. 18, No. 8, 08.2009, p. 1049-1063.

    Research output: Contribution to journalArticle

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