Alternating knot
In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link. A link is alternating if it has an alternating diagram. Many of the knots with crossing number less than 10 are alternating. This fact and useful properties of alternating knots, such as the Tait conjectures, was what enabled early knot tabulators, such as Tait, to construct tables with relatively few mistakes or omissions. The simplest non-alternating prime knots have 8 crossings (and there are three such: 819, 820, 821).
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6₃ knot888 (number)AlternatingAlternating diagramAlternating knot diagramAlternating knots and linksAlternating linkBorromean ringsChiral knotCrossing number (knot theory)Figure-eight knot (mathematics)FlypeHernando Burgos-SotoHistory of knot theoryHyperbolic linkKnot theoryList of geometric topology topicsList of knot theory topicsMarc LackenbyMathematical diagramMorwen ThistlethwaiteMénage problemPeter Tait (physicist)Skein relationSmall cancellation theorySplit linkTait's Knot ConjecturesTait conjecturesTorus knotTrefoil knotTurk's head knotTutte polynomialWilliam Menasco
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Alternating knot
In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link. A link is alternating if it has an alternating diagram. Many of the knots with crossing number less than 10 are alternating. This fact and useful properties of alternating knots, such as the Tait conjectures, was what enabled early knot tabulators, such as Tait, to construct tables with relatively few mistakes or omissions. The simplest non-alternating prime knots have 8 crossings (and there are three such: 819, 820, 821).
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En théorie des nœuds, un diagr ...... n-primalité du nœud/entrelacs.
@fr
Im mathematischen Gebiet der K ...... erschlingungsdiagramm besitzt.
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In knot theory, a knot or link ...... ces in a checker board manner.
@en
Na , um diagrama de nó ou enla ...... tiver um diagrama alternativo.
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В теории узлов диаграмма узла ...... диаграммы связаны с вершинами.
@ru
В теорії вузлів діаграма вузла ...... іаграми пов'язані з вершинами.
@uk
交代結び目(こうたいむすびめ、Alternating kno ...... knotに対して交互結び目という訳語がふられることもある。
@ja
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AlternatingKnot
@en
TaitsKnotConjectures
@en
title
Alternating Knot
@en
Tait's Knot Conjectures
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wikiPageUsesTemplate
comment
En théorie des nœuds, un diagr ...... n-primalité du nœud/entrelacs.
@fr
Im mathematischen Gebiet der K ...... nd Unterkreuzungen abwechseln.
@de
In knot theory, a knot or link ...... re three such: 819, 820, 821).
@en
Na , um diagrama de nó ou enla ...... tiver um diagrama alternativo.
@pt
В теории узлов диаграмма узла ...... диаграммы связаны с вершинами.
@ru
В теорії вузлів діаграма вузла ...... таких вузли — 819, 820, 821).
@uk
交代結び目(こうたいむすびめ、Alternating kno ...... knotに対して交互結び目という訳語がふられることもある。
@ja
label
Alternating knot
@en
Alternierendes Knotendiagramm
@de
Nó alternado
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Nœud alterné
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Альтернированный узел
@ru
Альтернований вузол
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交代結び目
@ja