k-alternating knots

P Hackney, Leonard Van Wyk, Nathan Walters

Research output: Contribution to journalArticle

1 Citation (Scopus)


A projection of a knot is k-alternating if its overcrossings and undercrossings alternate in groups of k as one reads around the projection (an obvious generalization of the notion of an alternating projection). We prove that every knot admits a 2-alternating projection, which partitions nontrivial knots into two classes: alternating and 2-alternating. © 2004 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)125-131
Number of pages7
JournalTopology and its Applications
Issue number1-3
Publication statusPublished - 14 May 2005
Externally publishedYes


  • knots
  • alternating knots
  • almost-alternating knots

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