K12a1166
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-q^7+2 q^6-3 q^5+3 q^4-4 q^3+4 q^2-4 q+4-3 q^{-1} +2 q^{-2} - q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -8 t+17-8 t^{-1} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-8 z^2 }[/math] |
| Determinant | 33 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4-z^2 a^2-2 z^2-2 z^2 a^{-2} -2 z^2 a^{-4} - a^{-4} -z^2 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +z^{10} a^{-2} +2 z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-1} -8 z^9 a^{-3} -8 z^9 a^{-5} +z^9 a^{-7} -6 z^8 a^{-2} -14 z^8 a^{-4} -6 z^8 a^{-6} +z^8 a^{-8} +z^8+a z^7-5 z^7 a^{-1} +26 z^7 a^{-3} +26 z^7 a^{-5} -6 z^7 a^{-7} +a^2 z^6+13 z^6 a^{-2} +36 z^6 a^{-4} +11 z^6 a^{-6} -7 z^6 a^{-8} -4 z^6+a^3 z^5-3 a z^5+9 z^5 a^{-1} -41 z^5 a^{-3} -44 z^5 a^{-5} +10 z^5 a^{-7} +a^4 z^4-2 a^2 z^4-10 z^4 a^{-2} -42 z^4 a^{-4} -8 z^4 a^{-6} +15 z^4 a^{-8} +6 z^4-2 a^3 z^3+4 a z^3-4 z^3 a^{-1} +28 z^3 a^{-3} +34 z^3 a^{-5} -4 z^3 a^{-7} -3 a^4 z^2+a^2 z^2+17 z^2 a^{-4} +3 z^2 a^{-6} -10 z^2 a^{-8} -8 z a^{-3} -8 z a^{-5} +a^4- a^{-4} + a^{-8} }[/math] |
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