K12n68

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^{10}+2 q^9-4 q^8+5 q^7-5 q^6+6 q^5-5 q^4+4 q^3-2 q^2+q }[/math]
Alexander polynomial	[math]\displaystyle{ -t^4+5 t^3-7 t^2+4 t-1+4 t^{-1} -7 t^{-2} +5 t^{-3} - t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -z^8-3 z^6+3 z^4+5 z^2+1 }[/math]
Determinant	35
Signature	6
HOMFLY-PT polynomial	[math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -6 z^6 a^{-6} +2 z^6 a^{-8} +5 z^4 a^{-4} -12 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +7 z^2 a^{-4} -12 z^2 a^{-6} +16 z^2 a^{-8} -6 z^2 a^{-10} +3 a^{-4} -5 a^{-6} +7 a^{-8} -5 a^{-10} + a^{-12} }[/math]
Kauffman polynomial	[math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +5 z^9 a^{-7} +3 z^9 a^{-9} +z^8 a^{-4} -z^8 a^{-6} +z^8 a^{-8} +3 z^8 a^{-10} -11 z^7 a^{-5} -26 z^7 a^{-7} -14 z^7 a^{-9} +z^7 a^{-11} -6 z^6 a^{-4} -16 z^6 a^{-6} -26 z^6 a^{-8} -16 z^6 a^{-10} +18 z^5 a^{-5} +38 z^5 a^{-7} +15 z^5 a^{-9} -5 z^5 a^{-11} +12 z^4 a^{-4} +36 z^4 a^{-6} +49 z^4 a^{-8} +25 z^4 a^{-10} -10 z^3 a^{-5} -20 z^3 a^{-7} -4 z^3 a^{-9} +6 z^3 a^{-11} -10 z^2 a^{-4} -24 z^2 a^{-6} -31 z^2 a^{-8} -18 z^2 a^{-10} -z^2 a^{-12} +z a^{-5} +4 z a^{-7} -3 z a^{-11} +3 a^{-4} +5 a^{-6} +7 a^{-8} +5 a^{-10} + a^{-12} }[/math]

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