K12a831

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ -q^5+4 q^4-11 q^3+19 q^2-26 q+32-32 q^{-1} +30 q^{-2} -23 q^{-3} +15 q^{-4} -8 q^{-5} +3 q^{-6} - q^{-7} }[/math]
Alexander polynomial	[math]\displaystyle{ 2 t^4-9 t^3+24 t^2-42 t+51-42 t^{-1} +24 t^{-2} -9 t^{-3} +2 t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ 2 z^8+7 z^6+10 z^4+5 z^2+1 }[/math]
Determinant	205
Signature	0
HOMFLY-PT polynomial	[math]\displaystyle{ a^2 z^8+z^8-a^4 z^6+5 a^2 z^6-z^6 a^{-2} +4 z^6-4 a^4 z^4+11 a^2 z^4-3 z^4 a^{-2} +6 z^4-6 a^4 z^2+11 a^2 z^2-4 z^2 a^{-2} +4 z^2-3 a^4+4 a^2-2 a^{-2} +2 }[/math]
Kauffman polynomial	[math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+13 a^2 z^{10}+8 z^{10}+5 a^5 z^9+10 a^3 z^9+19 a z^9+14 z^9 a^{-1} +3 a^6 z^8-9 a^4 z^8-25 a^2 z^8+15 z^8 a^{-2} +2 z^8+a^7 z^7-14 a^5 z^7-39 a^3 z^7-52 a z^7-18 z^7 a^{-1} +10 z^7 a^{-3} -10 a^6 z^6+2 a^4 z^6+15 a^2 z^6-25 z^6 a^{-2} +4 z^6 a^{-4} -26 z^6-4 a^7 z^5+12 a^5 z^5+46 a^3 z^5+46 a z^5+z^5 a^{-1} -14 z^5 a^{-3} +z^5 a^{-5} +10 a^6 z^4-2 a^4 z^4-12 a^2 z^4+19 z^4 a^{-2} -3 z^4 a^{-4} +22 z^4+5 a^7 z^3-5 a^5 z^3-29 a^3 z^3-20 a z^3+10 z^3 a^{-1} +10 z^3 a^{-3} -z^3 a^{-5} -3 a^6 z^2+6 a^4 z^2+10 a^2 z^2-8 z^2 a^{-2} -7 z^2-2 a^7 z+2 a^5 z+8 a^3 z+3 a z-5 z a^{-1} -4 z a^{-3} -3 a^4-4 a^2+2 a^{-2} +2 }[/math]

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