Knot diagrams on a punctured sphere as a model of string figures

Masafumi Arai, Kouki Taniyama

Research output: Contribution to journalArticlepeer-review


A string figure is topologically a trivial knot lying on an imaginary plane orthogonal to the fingers with some crossings. The fingers prevent cancellation of these crossings. As a mathematical model of string figure, we consider a knot diagram on the xy-plane in xyz-space missing some straight lines parallel to the z-axis. These straight lines correspond to fingers. We study minimal number of crossings of these knot diagrams under Reidemeister moves missing these lines.

Original languageEnglish
Article number2050071
JournalJournal of Knot Theory and its Ramifications
Issue number11
Publication statusPublished - 2020 Oct


  • Knot
  • Reidemeister move
  • Turaev cobracket
  • crossing number
  • knot diagram
  • minimal self-intersection number
  • string figure

ASJC Scopus subject areas

  • Algebra and Number Theory


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