k-alternating knots

P Hackney; Leonard Van Wyk; Nathan Walters

doi:10.1016/j.topol.2004.11.007

k-alternating knots

P Hackney, Leonard Van Wyk, Nathan Walters

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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. &COPY; 2004 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	125-131
Number of pages	7
Journal	Topology and its Applications
Volume	150
Issue number	1-3
DOIs	https://doi.org/10.1016/j.topol.2004.11.007
Publication status	Published - 14 May 2005
Externally published	Yes

Keywords

knots
alternating knots
almost-alternating knots
LINKS

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10.1016/j.topol.2004.11.007

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title = "k-alternating knots",

abstract = "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. &COPY; 2004 Elsevier B.V. All rights reserved.",

keywords = "knots, alternating knots, almost-alternating knots, LINKS",

author = "P Hackney and {Van Wyk}, Leonard and Nathan Walters",

year = "2005",

month = may,

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doi = "10.1016/j.topol.2004.11.007",

language = "English",

volume = "150",

pages = "125--131",

journal = "Topology and its Applications",

issn = "0166-8641",

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T1 - k-alternating knots

AU - Hackney, P

AU - Van Wyk, Leonard

AU - Walters, Nathan

PY - 2005/5/14

Y1 - 2005/5/14

N2 - 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. &COPY; 2004 Elsevier B.V. All rights reserved.

AB - 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. &COPY; 2004 Elsevier B.V. All rights reserved.

KW - knots

KW - alternating knots

KW - almost-alternating knots

KW - LINKS

U2 - 10.1016/j.topol.2004.11.007

DO - 10.1016/j.topol.2004.11.007

M3 - Article

SN - 0166-8641

VL - 150

SP - 125

EP - 131

JO - Topology and its Applications

JF - Topology and its Applications

IS - 1-3

ER -

k-alternating knots

Abstract

Keywords

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