K12n516
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-5 q^9+9 q^8-13 q^7+16 q^6-16 q^5+15 q^4-11 q^3+7 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+11 t^2-22 t+27-22 t^{-1} +11 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-z^4+4 z^2+1 }[/math] |
| Determinant | 97 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} +z^4 a^{-2} -2 z^4 a^{-4} -z^4 a^{-6} +z^4 a^{-8} +2 z^2 a^{-2} -z^2 a^{-4} +3 z^2 a^{-6} + a^{-2} - a^{-4} +3 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +3 z^9 a^{-5} +5 z^9 a^{-7} +2 z^9 a^{-9} +4 z^8 a^{-4} +6 z^8 a^{-6} +3 z^8 a^{-8} +z^8 a^{-10} +3 z^7 a^{-3} -3 z^7 a^{-7} +z^6 a^{-2} -7 z^6 a^{-4} -11 z^6 a^{-6} +2 z^6 a^{-8} +5 z^6 a^{-10} -8 z^5 a^{-3} -12 z^5 a^{-5} -4 z^5 a^{-7} +5 z^5 a^{-9} +5 z^5 a^{-11} -3 z^4 a^{-2} -z^4 a^{-4} -4 z^4 a^{-6} -12 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +6 z^3 a^{-3} +9 z^3 a^{-5} -z^3 a^{-7} -7 z^3 a^{-9} -3 z^3 a^{-11} +3 z^2 a^{-2} +4 z^2 a^{-4} +9 z^2 a^{-6} +9 z^2 a^{-8} +z^2 a^{-10} -z a^{-3} -2 z a^{-5} +2 z a^{-7} +2 z a^{-9} -z a^{-11} - a^{-2} - a^{-4} -3 a^{-6} -2 a^{-8} }[/math] |
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