K12a170
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+9 q^7-15 q^6+22 q^5-27 q^4+28 q^3-26 q^2+21 q-14+8 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-18 t^2+42 t-53+42 t^{-1} -18 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6-3 z^2+1 }[/math] |
| Determinant | 179 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} -z^4 a^{-2} +6 z^4 a^{-4} -3 z^4 a^{-6} -2 z^4+a^2 z^2-6 z^2 a^{-2} +9 z^2 a^{-4} -6 z^2 a^{-6} +z^2 a^{-8} -2 z^2+a^2-4 a^{-2} +5 a^{-4} -3 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +4 z^{10} a^{-2} +8 z^{10} a^{-4} +4 z^{10} a^{-6} +6 z^9 a^{-1} +14 z^9 a^{-3} +15 z^9 a^{-5} +7 z^9 a^{-7} +2 z^8 a^{-2} -3 z^8 a^{-4} +7 z^8 a^{-6} +7 z^8 a^{-8} +5 z^8+3 a z^7-10 z^7 a^{-1} -39 z^7 a^{-3} -39 z^7 a^{-5} -9 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-19 z^6 a^{-2} -28 z^6 a^{-4} -35 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -9 z^6-7 a z^5+7 z^5 a^{-1} +44 z^5 a^{-3} +35 z^5 a^{-5} -4 z^5 a^{-7} -9 z^5 a^{-9} -3 a^2 z^4+27 z^4 a^{-2} +48 z^4 a^{-4} +38 z^4 a^{-6} +9 z^4 a^{-8} -2 z^4 a^{-10} +3 z^4+4 a z^3-7 z^3 a^{-1} -20 z^3 a^{-3} -9 z^3 a^{-5} +5 z^3 a^{-7} +5 z^3 a^{-9} +3 a^2 z^2-19 z^2 a^{-2} -26 z^2 a^{-4} -16 z^2 a^{-6} -4 z^2 a^{-8} +z^2 a^{-10} -z^2+2 z a^{-1} +2 z a^{-3} -z a^{-7} -z a^{-9} -a^2+4 a^{-2} +5 a^{-4} +3 a^{-6} + a^{-8} +1 }[/math] |
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