K12a1247

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^9+3 q^8-6 q^7+10 q^6-14 q^5+16 q^4-17 q^3+17 q^2-13 q+10-6 q^{-1} +3 q^{-2} - q^{-3} }[/math]
Alexander polynomial	[math]\displaystyle{ 2 t^4-8 t^3+16 t^2-21 t+23-21 t^{-1} +16 t^{-2} -8 t^{-3} +2 t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ 2 z^8+8 z^6+8 z^4+3 z^2+1 }[/math]
Determinant	117
Signature	4
HOMFLY-PT polynomial	[math]\displaystyle{ z^8 a^{-2} +z^8 a^{-4} +5 z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -z^6+8 z^4 a^{-2} +8 z^4 a^{-4} -4 z^4 a^{-6} -4 z^4+6 z^2 a^{-2} +5 z^2 a^{-4} -4 z^2 a^{-6} -4 z^2+3 a^{-2} - a^{-6} -1 }[/math]
Kauffman polynomial	[math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +10 z^{10} a^{-2} +7 z^{10} a^{-4} +3 z^{10}+a z^9-5 z^9 a^{-1} +6 z^9 a^{-3} +12 z^9 a^{-5} -50 z^8 a^{-2} -17 z^8 a^{-4} +15 z^8 a^{-6} -18 z^8-6 a z^7-15 z^7 a^{-1} -58 z^7 a^{-3} -35 z^7 a^{-5} +14 z^7 a^{-7} +78 z^6 a^{-2} -11 z^6 a^{-4} -42 z^6 a^{-6} +10 z^6 a^{-8} +37 z^6+13 a z^5+55 z^5 a^{-1} +96 z^5 a^{-3} +17 z^5 a^{-5} -31 z^5 a^{-7} +6 z^5 a^{-9} -42 z^4 a^{-2} +33 z^4 a^{-4} +29 z^4 a^{-6} -13 z^4 a^{-8} +3 z^4 a^{-10} -30 z^4-12 a z^3-48 z^3 a^{-1} -52 z^3 a^{-3} +4 z^3 a^{-5} +16 z^3 a^{-7} -3 z^3 a^{-9} +z^3 a^{-11} +9 z^2 a^{-2} -11 z^2 a^{-4} -9 z^2 a^{-6} +2 z^2 a^{-8} +9 z^2+4 a z+11 z a^{-1} +10 z a^{-3} -3 z a^{-7} -3 a^{-2} + a^{-6} -1 }[/math]

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