K12n542
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+5 q-10+15 q^{-1} -18 q^{-2} +20 q^{-3} -18 q^{-4} +14 q^{-5} -9 q^{-6} +4 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-9 t^2+28 t-39+28 t^{-1} -9 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-3 z^4+z^2+1 }[/math] |
| Determinant | 115 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^8+4 z^2 a^6+3 a^6-4 z^4 a^4-7 z^2 a^4-4 a^4+z^6 a^2+2 z^4 a^2+4 z^2 a^2+3 a^2-z^4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^6 z^{10}+a^4 z^{10}+a^7 z^9+6 a^5 z^9+5 a^3 z^9+2 a^6 z^8+12 a^4 z^8+10 a^2 z^8+a^7 z^7-4 a^5 z^7+5 a^3 z^7+10 a z^7+4 a^8 z^6+2 a^6 z^6-19 a^4 z^6-12 a^2 z^6+5 z^6+a^9 z^5+2 a^7 z^5-4 a^5 z^5-21 a^3 z^5-15 a z^5+z^5 a^{-1} -6 a^8 z^4-9 a^6 z^4-2 a^4 z^4-4 a^2 z^4-5 z^4-2 a^9 z^3-5 a^7 z^3+4 a^5 z^3+10 a^3 z^3+3 a z^3+2 a^8 z^2+9 a^6 z^2+14 a^4 z^2+7 a^2 z^2+a^9 z+a^7 z-a^8-3 a^6-4 a^4-3 a^2 }[/math] |
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