K12a1221

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^8+4 q^7-9 q^6+16 q^5-24 q^4+29 q^3-30 q^2+29 q-23+16 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math]
Alexander polynomial	[math]\displaystyle{ t^5-5 t^4+13 t^3-24 t^2+35 t-39+35 t^{-1} -24 t^{-2} +13 t^{-3} -5 t^{-4} + t^{-5} }[/math]
Conway polynomial	[math]\displaystyle{ z^{10}+5 z^8+8 z^6+4 z^4+z^2+1 }[/math]
Determinant	195
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ z^{10} a^{-2} +7 z^8 a^{-2} -z^8 a^{-4} -z^8+18 z^6 a^{-2} -5 z^6 a^{-4} -5 z^6+20 z^4 a^{-2} -8 z^4 a^{-4} -8 z^4+9 z^2 a^{-2} -4 z^2 a^{-4} -4 z^2+2 a^{-2} - a^{-4} }[/math]
Kauffman polynomial	[math]\displaystyle{ 3 z^{11} a^{-1} +3 z^{11} a^{-3} +15 z^{10} a^{-2} +8 z^{10} a^{-4} +7 z^{10}+7 a z^9+4 z^9 a^{-1} +8 z^9 a^{-3} +11 z^9 a^{-5} +4 a^2 z^8-43 z^8 a^{-2} -9 z^8 a^{-4} +11 z^8 a^{-6} -19 z^8+a^3 z^7-22 a z^7-27 z^7 a^{-1} -27 z^7 a^{-3} -15 z^7 a^{-5} +8 z^7 a^{-7} -13 a^2 z^6+55 z^6 a^{-2} +4 z^6 a^{-4} -16 z^6 a^{-6} +4 z^6 a^{-8} +18 z^6-3 a^3 z^5+20 a z^5+29 z^5 a^{-1} +22 z^5 a^{-3} +4 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4-44 z^4 a^{-2} -6 z^4 a^{-4} +8 z^4 a^{-6} -5 z^4 a^{-8} -14 z^4+2 a^3 z^3-6 a z^3-15 z^3 a^{-1} -7 z^3 a^{-3} +6 z^3 a^{-5} +5 z^3 a^{-7} -z^3 a^{-9} -a^2 z^2+14 z^2 a^{-2} +6 z^2 a^{-4} +z^2 a^{-8} +6 z^2+a z+2 z a^{-1} +z a^{-3} -z a^{-5} -z a^{-7} -2 a^{-2} - a^{-4} }[/math]

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