K12a1252

Dowker-Thistlethwaite code

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

Jones polynomial	[math]\displaystyle{ q^9-4 q^8+11 q^7-20 q^6+28 q^5-35 q^4+37 q^3-34 q^2+28 q-18+10 q^{-1} -4 q^{-2} + q^{-3} }[/math]
Alexander polynomial	[math]\displaystyle{ -2 t^4+10 t^3-27 t^2+48 t-57+48 t^{-1} -27 t^{-2} +10 t^{-3} -2 t^{-4} }[/math]
Conway polynomial	[math]\displaystyle{ -2 z^8-6 z^6-7 z^4-2 z^2+1 }[/math]
Determinant	231
Signature	2
HOMFLY-PT polynomial	[math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +z^6-6 z^4 a^{-2} -7 z^4 a^{-4} +3 z^4 a^{-6} +3 z^4-2 z^2 a^{-2} -7 z^2 a^{-4} +4 z^2 a^{-6} +3 z^2+2 a^{-2} -4 a^{-4} +2 a^{-6} +1 }[/math]
Kauffman polynomial	[math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +8 z^{10} a^{-2} +17 z^{10} a^{-4} +9 z^{10} a^{-6} +10 z^9 a^{-1} +14 z^9 a^{-3} +16 z^9 a^{-5} +12 z^9 a^{-7} -6 z^8 a^{-2} -31 z^8 a^{-4} -8 z^8 a^{-6} +9 z^8 a^{-8} +8 z^8+4 a z^7-17 z^7 a^{-1} -38 z^7 a^{-3} -45 z^7 a^{-5} -24 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-6 z^6 a^{-2} +25 z^6 a^{-4} -5 z^6 a^{-6} -18 z^6 a^{-8} +z^6 a^{-10} -16 z^6-8 a z^5+10 z^5 a^{-1} +34 z^5 a^{-3} +44 z^5 a^{-5} +21 z^5 a^{-7} -7 z^5 a^{-9} -2 a^2 z^4+6 z^4 a^{-2} -19 z^4 a^{-4} +3 z^4 a^{-6} +13 z^4 a^{-8} -2 z^4 a^{-10} +11 z^4+4 a z^3-4 z^3 a^{-1} -16 z^3 a^{-3} -26 z^3 a^{-5} -15 z^3 a^{-7} +3 z^3 a^{-9} +a^2 z^2+13 z^2 a^{-4} +2 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -4 z^2+z a^{-1} +5 z a^{-3} +9 z a^{-5} +5 z a^{-7} -2 a^{-2} -4 a^{-4} -2 a^{-6} +1 }[/math]

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