K12n84

Dowker-Thistlethwaite code

4 8 12 2 16 6 -18 -22 10 -24 -14 -20

Jones polynomial	[math]\displaystyle{ -q^6+2 q^5-5 q^4+8 q^3-9 q^2+11 q-9+8 q^{-1} -6 q^{-2} +3 q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ 2 t^3-7 t^2+14 t-17+14 t^{-1} -7 t^{-2} +2 t^{-3} }[/math]
Conway polynomial	[math]\displaystyle{ 2 z^6+5 z^4+4 z^2+1 }[/math]
Determinant	63
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ z^6 a^{-2} +z^6-a^2 z^4+4 z^4 a^{-2} -z^4 a^{-4} +3 z^4-2 a^2 z^2+7 z^2 a^{-2} -3 z^2 a^{-4} +2 z^2-a^2+5 a^{-2} -3 a^{-4} }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{10} a^{-2} +z^{10}+3 a z^9+5 z^9 a^{-1} +2 z^9 a^{-3} +3 a^2 z^8+z^8 a^{-2} +z^8 a^{-4} +3 z^8+a^3 z^7-9 a z^7-16 z^7 a^{-1} -6 z^7 a^{-3} -12 a^2 z^6-10 z^6 a^{-2} -22 z^6-4 a^3 z^5+a z^5+12 z^5 a^{-1} +11 z^5 a^{-3} +4 z^5 a^{-5} +13 a^2 z^4+8 z^4 a^{-2} -z^4 a^{-4} +2 z^4 a^{-6} +24 z^4+5 a^3 z^3+7 a z^3-5 z^3 a^{-1} -13 z^3 a^{-3} -5 z^3 a^{-5} +z^3 a^{-7} -5 a^2 z^2+3 z^2 a^{-2} +4 z^2 a^{-4} -z^2 a^{-6} -7 z^2-2 a^3 z-2 a z+3 z a^{-1} +7 z a^{-3} +3 z a^{-5} -z a^{-7} +a^2-5 a^{-2} -3 a^{-4} }[/math]

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