K12n428
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+2 q^9-3 q^8+4 q^7-5 q^6+5 q^5-4 q^4+4 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-5 t^2+4 t-3+4 t^{-1} -5 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-z^4+4 z^2+1 }[/math] |
| Determinant | 31 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -6 z^6 a^{-6} +z^6 a^{-8} +5 z^4 a^{-4} -11 z^4 a^{-6} +5 z^4 a^{-8} +7 z^2 a^{-4} -8 z^2 a^{-6} +6 z^2 a^{-8} -z^2 a^{-10} +3 a^{-4} -3 a^{-6} +2 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +4 z^9 a^{-7} +2 z^9 a^{-9} +z^8 a^{-4} -2 z^8 a^{-6} -2 z^8 a^{-8} +z^8 a^{-10} -11 z^7 a^{-5} -21 z^7 a^{-7} -10 z^7 a^{-9} -6 z^6 a^{-4} -11 z^6 a^{-6} -9 z^6 a^{-8} -4 z^6 a^{-10} +17 z^5 a^{-5} +31 z^5 a^{-7} +15 z^5 a^{-9} +z^5 a^{-11} +12 z^4 a^{-4} +28 z^4 a^{-6} +20 z^4 a^{-8} +4 z^4 a^{-10} -7 z^3 a^{-5} -16 z^3 a^{-7} -12 z^3 a^{-9} -3 z^3 a^{-11} -10 z^2 a^{-4} -17 z^2 a^{-6} -12 z^2 a^{-8} -4 z^2 a^{-10} +z^2 a^{-12} +3 z a^{-7} +3 z a^{-9} +z a^{-11} +z a^{-13} +3 a^{-4} +3 a^{-6} +2 a^{-8} + a^{-10} }[/math] |
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