Torus Knot Splice Base: Difference between revisions
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|'''[[Gauss Codes|Gauss code]]''' |
|'''[[Gauss Codes|Gauss code]]''' |
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|style="padding-left: 1em;" | <*GaussCode[K]*> |
|style="padding-left: 1em;" | <*List @@ GaussCode[K]*> |
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|'''[[DT (Dowker-Thistlethwaite) Codes|Dowker-Thistlethwaite code]]''' |
|'''[[DT (Dowker-Thistlethwaite) Codes|Dowker-Thistlethwaite code]]''' |
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|style="padding-left: 1em;" | <*DTCode[K]*> |
|style="padding-left: 1em;" | <*StringReplace[StringTake[ToString[DTCode[K]], {8, -2}], ","->""]*> |
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===Polynomial invariants=== |
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{| style="margin-left: 1em;" |
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|'''[[The Jones Polynomial|Jones polynomial]]''' |
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|style="padding-left: 1em;" | {{Data:7_5/Jones Polynomial}} |
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|'''[[The Alexander-Conway Polynomial|Alexander polynomial]]''' |
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|style="padding-left: 1em;" | {{Data:7_5/Alexander Polynomial}} |
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|'''[[The Alexander-Conway Polynomial|Conway polynomial]]''' |
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|style="padding-left: 1em;" | {{Data:7_5/Conway Polynomial}} |
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|'''[[The Determinant and the Signature|Determinant]]''' |
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|style="padding-left: 1em;" | {{Data:7_5/Determinant}} |
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|'''[[The Determinant and the Signature|Signature]]''' |
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|style="padding-left: 1em;" | {{Data:7_5/Signature}} |
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|'''[[The HOMFLY-PT Polynomial|HOMFLY-PT polynomial]]''' |
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|style="padding-left: 1em;" | {{Data:7_5/HOMFLYPT Polynomial}} |
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|'''[[The Kauffman Polynomial|Kauffman polynomial]]''' |
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|style="padding-left: 1em;" | {{Data:7_5/Kauffman Polynomial}} |
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| ([[Viewing Knot Invariants in Other Formats|other formats]]) |
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===[[Finite Type (Vassiliev) Invariants|Vassiliev invariants]]=== |
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{| style="margin-left: 1em;" |
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|'''V<sub>2</sub> and V<sub>3</sub>''' |
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|style="padding-left: 1em;" | ({{Data:7_5/V_2}}, {{Data:7_5/V_3}}) |
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{{subst:Khovanov Invariants|name=7_5}} |
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{{subst:Quantum Invariants|name=7_5}} |
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Revision as of 15:04, 26 August 2005
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[[Image:Data:Torus Knot Splice Base/Previous Knot.{{{ext}}}|80px|link=Data:Torus Knot Splice Base/Previous Knot]] |
[[Image:Data:Torus Knot Splice Base/Next Knot.{{{ext}}}|80px|link=Data:Torus Knot Splice Base/Next Knot]] |
Visit [<*KnotilusURL[K]<>" "<>ThisKnot*>'s page] at Knotilus!
Visit <*m*>.<*n*>.html <*ThisKnot*>'s page at the original Knot Atlas!
Knot presentations
| Planar diagram presentation | <*PD[K]*> |
| Gauss code | <*List @@ GaussCode[K]*> |
| Dowker-Thistlethwaite code | <*StringReplace[StringTake[ToString[DTCode[K]], {8, -2}], ","->""]*> |
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ - q^{-9} +2 q^{-8} -3 q^{-7} +3 q^{-6} -3 q^{-5} +3 q^{-4} - q^{-3} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^2-4 t+5-4 t^{-1} +2 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^4+4 z^2+1 }[/math] |
| Determinant | 17 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^8 \left(-z^2\right)-a^8+a^6 z^4+2 a^6 z^2+a^4 z^4+3 a^4 z^2+2 a^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^{11} z^3-a^{11} z+2 a^{10} z^4-2 a^{10} z^2+2 a^9 z^5-2 a^9 z^3+a^9 z+a^8 z^6+a^8 z^2-a^8+3 a^7 z^5-4 a^7 z^3+a^7 z+a^6 z^6-a^6 z^4+a^5 z^5-a^5 z^3-a^5 z+a^4 z^4-3 a^4 z^2+2 a^4 }[/math] |
| (other formats) |
Vassiliev invariants
| V2 and V3 | (4, -8) |
{{subst:Khovanov Invariants|name=7_5}}
{{subst:Quantum Invariants|name=7_5}}
