A partial ordering of knots and links through diagrammatic unknotting

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State: Public
Version: Author's accepted manuscript
Serval ID
serval:BIB_E9F6D0EED72F
Type
Article: article from journal or magazin.
Collection
Publications
Institution
Title
A partial ordering of knots and links through diagrammatic unknotting
Journal
Journal of Knot Theory and its Ramifications
Author(s)
Diao Y., Ernst C., Stasiak A.
ISSN
0218-2165
Publication state
Published
Issued date
2009
Peer-reviewed
Oui
Volume
18
Number
4
Pages
505-522
Language
english
Abstract
In this paper we de. ne a partial ordering of knots and links using a special property derived from their minimal diagrams. A link K' is called a predecessor of a link K if Cr(K') < Cr(K) and a diagram of K' can be obtained from a minimal diagram D of K by a single crossing change. In such a case, we say that K' < K. We investigate the sets of links that can be obtained by single crossing changes over all minimal diagrams of a given link. We show that these sets are specific for different links and permit partial ordering of all links. Some interesting results are presented and many questions are raised.
Keywords
Knots, links, crossing number, unknotting number, UNLINKING NUMBER, 2-BRIDGE KNOTS, CLASSIFICATION
Web of science
Open Access
Yes
Create date
09/11/2009 13:08
Last modification date
20/08/2019 16:12
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