Torus Knot Splice Base

[[Image:Data:Torus Knot Splice Base/Previous Knot.{{{ext}}}|80px|link=Data:Torus Knot Splice Base/Previous Knot]] [[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]] [[Data:Torus Knot Splice Base/Next Knot]]

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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}}