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	$-q^{-9}+2q^{-8}-3q^{-7}+3q^{-6}-3q^{-5}+3q^{-4}-q^{-3}+q^{-2}$
Alexander polynomial	$2t^{2}-4t+5-4t^{-1}+2t^{-2}$
Conway polynomial	$2z^{4}+4z^{2}+1$
Determinant	17
Signature	-4
HOMFLY-PT polynomial	$a^{8}\left(-z^{2}\right)-a^{8}+a^{6}z^{4}+2a^{6}z^{2}+a^{4}z^{4}+3a^{4}z^{2}+2a^{4}$
Kauffman polynomial	$a^{11}z^{3}-a^{11}z+2a^{10}z^{4}-2a^{10}z^{2}+2a^{9}z^{5}-2a^{9}z^{3}+a^{9}z+a^{8}z^{6}+a^{8}z^{2}-a^{8}+3a^{7}z^{5}-4a^{7}z^{3}+a^{7}z+a^{6}z^{6}-a^{6}z^{4}+a^{5}z^{5}-a^{5}z^{3}-a^{5}z+a^{4}z^{4}-3a^{4}z^{2}+2a^{4}$
(other formats)

Vassiliev invariants

V2 and V3

(4, -8)

{{subst:Khovanov Invariants|name=7_5}}

{{subst:Quantum Invariants|name=7_5}}