K12a545
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-7 q^6+12 q^5-17 q^4+21 q^3-22 q^2+21 q-16+12 q^{-1} -7 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-16 t^2+32 t-39+32 t^{-1} -16 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+8 z^4+4 z^2+1 }[/math] |
| Determinant | 143 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+6 z^4 a^{-2} +2 z^4 a^{-4} -z^4 a^{-6} +2 z^4-2 a^2 z^2+6 z^2 a^{-2} +z^2 a^{-4} -2 z^2 a^{-6} +z^2-a^2+2 a^{-2} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +6 z^{10} a^{-2} +3 z^{10} a^{-4} +3 z^{10}+4 a z^9+6 z^9 a^{-1} +7 z^9 a^{-3} +5 z^9 a^{-5} +3 a^2 z^8-9 z^8 a^{-2} +3 z^8 a^{-4} +6 z^8 a^{-6} -3 z^8+a^3 z^7-11 a z^7-20 z^7 a^{-1} -16 z^7 a^{-3} -3 z^7 a^{-5} +5 z^7 a^{-7} -11 a^2 z^6-2 z^6 a^{-2} -13 z^6 a^{-4} -8 z^6 a^{-6} +3 z^6 a^{-8} -11 z^6-4 a^3 z^5+4 a z^5+12 z^5 a^{-1} +9 z^5 a^{-3} -3 z^5 a^{-5} -7 z^5 a^{-7} +z^5 a^{-9} +12 a^2 z^4+3 z^4 a^{-2} +13 z^4 a^{-4} +6 z^4 a^{-6} -5 z^4 a^{-8} +13 z^4+5 a^3 z^3+5 a z^3+5 z^3 a^{-5} +3 z^3 a^{-7} -2 z^3 a^{-9} -5 a^2 z^2+3 z^2 a^{-2} -4 z^2 a^{-4} -4 z^2 a^{-6} +2 z^2 a^{-8} -4 z^2-2 a^3 z-3 a z-z a^{-1} -2 z a^{-5} -z a^{-7} +z a^{-9} +a^2-2 a^{-2} + a^{-6} +1 }[/math] |
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