K13n2885

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Polynomial invariants

Jones polynomial Data:K13n2885/Jones Polynomial
Alexander polynomial [math]\displaystyle{ t^4-4 t^3+9 t^2-16 t+21-16 t^{-1} +9 t^{-2} -4 t^{-3} + t^{-4} }[/math]
Conway polynomial Data:K13n2885/Conway Polynomial
Determinant 81
Signature 0
HOMFLY-PT polynomial [math]\displaystyle{ z^8 a^{-2} +6 z^6 a^{-2} -z^6 a^{-4} -z^6+13 z^4 a^{-2} -4 z^4 a^{-4} -4 z^4+11 z^2 a^{-2} -5 z^2 a^{-4} -6 z^2+a^2+3 a^{-2} - a^{-4} -2 }[/math]
Kauffman polynomial [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +4 z^{10} a^{-2} +3 z^{10} a^{-4} +z^{10}-4 z^9 a^{-1} +4 z^9 a^{-5} -17 z^8 a^{-2} -10 z^8 a^{-4} +3 z^8 a^{-6} -4 z^8+2 a z^7+12 z^7 a^{-1} -6 z^7 a^{-3} -15 z^7 a^{-5} +z^7 a^{-7} +35 z^6 a^{-2} +12 z^6 a^{-4} -12 z^6 a^{-6} +11 z^6-4 a z^5-18 z^5 a^{-1} +6 z^5 a^{-3} +16 z^5 a^{-5} -4 z^5 a^{-7} +3 a^2 z^4-41 z^4 a^{-2} -14 z^4 a^{-4} +13 z^4 a^{-6} -11 z^4+a^3 z^3+9 a z^3+12 z^3 a^{-1} -8 z^3 a^{-3} -8 z^3 a^{-5} +4 z^3 a^{-7} -a^2 z^2+19 z^2 a^{-2} +6 z^2 a^{-4} -3 z^2 a^{-6} +9 z^2-a^3 z-3 a z-z a^{-1} +3 z a^{-3} +2 z a^{-5} -a^2-3 a^{-2} - a^{-4} -2 }[/math]



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