k-alternating knots

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...

Full description

Saved in:
Bibliographic Details
Published in:Topology and its applications 2005-05, Vol.150 (1), p.125-131
Main Authors: Hackney, Philip, Van Wyk, Leonard, Walters, Nathan
Format: Article
Language:English
Subjects:
Almost-alternating knots
Alternating knots
Knots
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0166-8641
1879-3207
DOI:10.1016/j.topol.2004.11.007