K12n419
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+2 q^{10}-2 q^9+q^8-q^7+2 q^5-2 q^4+3 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-3 t^2-3 t+7-3 t^{-1} -3 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6+z^4+5 z^2+1 }[/math] |
| Determinant | 3 |
| 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} -10 z^4 a^{-6} +6 z^4 a^{-8} +6 z^2 a^{-4} -6 z^2 a^{-6} +7 z^2 a^{-8} -2 z^2 a^{-10} +2 a^{-4} - a^{-6} + a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +3 z^9 a^{-7} +z^9 a^{-9} +z^8 a^{-4} -4 z^8 a^{-6} -5 z^8 a^{-8} -12 z^7 a^{-5} -19 z^7 a^{-7} -6 z^7 a^{-9} +z^7 a^{-11} -6 z^6 a^{-4} -3 z^6 a^{-6} +z^6 a^{-8} +2 z^6 a^{-12} +20 z^5 a^{-5} +31 z^5 a^{-7} +6 z^5 a^{-9} -4 z^5 a^{-11} +z^5 a^{-13} +11 z^4 a^{-4} +17 z^4 a^{-6} +11 z^4 a^{-8} -2 z^4 a^{-10} -7 z^4 a^{-12} -10 z^3 a^{-5} -14 z^3 a^{-7} +z^3 a^{-9} +2 z^3 a^{-11} -3 z^3 a^{-13} -8 z^2 a^{-4} -11 z^2 a^{-6} -7 z^2 a^{-8} -z^2 a^{-10} +3 z^2 a^{-12} +2 z a^{-7} -z a^{-11} +z a^{-13} +2 a^{-4} + a^{-6} + a^{-8} + a^{-10} }[/math] |
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