K12n42
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+5 q^7-7 q^6+9 q^5-10 q^4+9 q^3-7 q^2+5 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-6 t^2+14 t-17+14 t^{-1} -6 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-z^2+1 }[/math] |
| Determinant | 59 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-4} -2 z^4 a^{-2} +4 z^4 a^{-4} -2 z^4 a^{-6} -5 z^2 a^{-2} +7 z^2 a^{-4} -5 z^2 a^{-6} +z^2 a^{-8} +z^2-3 a^{-2} +4 a^{-4} -3 a^{-6} + a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +2 z^9 a^{-3} +5 z^9 a^{-5} +3 z^9 a^{-7} +z^8 a^{-2} -z^8 a^{-4} +2 z^8 a^{-6} +4 z^8 a^{-8} -10 z^7 a^{-3} -22 z^7 a^{-5} -9 z^7 a^{-7} +3 z^7 a^{-9} -4 z^6 a^{-2} -9 z^6 a^{-4} -20 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} +2 z^5 a^{-1} +22 z^5 a^{-3} +35 z^5 a^{-5} +5 z^5 a^{-7} -10 z^5 a^{-9} +11 z^4 a^{-2} +28 z^4 a^{-4} +33 z^4 a^{-6} +12 z^4 a^{-8} -3 z^4 a^{-10} +z^4-4 z^3 a^{-1} -16 z^3 a^{-3} -18 z^3 a^{-5} +6 z^3 a^{-9} -12 z^2 a^{-2} -20 z^2 a^{-4} -17 z^2 a^{-6} -5 z^2 a^{-8} +z^2 a^{-10} -3 z^2+z a^{-1} +3 z a^{-3} +3 z a^{-5} -z a^{-9} +3 a^{-2} +4 a^{-4} +3 a^{-6} + a^{-8} +2 }[/math] |
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