K12a1278
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^4-q^3+2 q^2-3 q+4-5 q^{-1} +5 q^{-2} -5 q^{-3} +5 q^{-4} -4 q^{-5} +3 q^{-6} -2 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+7 t^2-7 t+7-7 t^{-1} +7 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-11 z^4-6 z^2+1 }[/math] |
| Determinant | 41 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^6+3 z^2 a^6+a^6-z^6 a^4-4 z^4 a^4-3 z^2 a^4-z^6 a^2-4 z^4 a^2-3 z^2 a^2-z^6-5 z^4-7 z^2-3+z^4 a^{-2} +4 z^2 a^{-2} +3 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +2 a^2 z^{10}+z^{10} a^{-2} +3 z^{10}+3 a^3 z^9-5 a z^9-8 z^9 a^{-1} +4 a^4 z^8-10 a^2 z^8-9 z^8 a^{-2} -23 z^8+5 a^5 z^7-13 a^3 z^7+4 a z^7+22 z^7 a^{-1} +5 a^6 z^6-15 a^4 z^6+12 a^2 z^6+29 z^6 a^{-2} +61 z^6+4 a^7 z^5-17 a^5 z^5+12 a^3 z^5+9 a z^5-24 z^5 a^{-1} +3 a^8 z^4-13 a^6 z^4+11 a^4 z^4+a^2 z^4-40 z^4 a^{-2} -66 z^4+2 a^9 z^3-6 a^7 z^3+13 a^5 z^3+2 a^3 z^3-10 a z^3+9 z^3 a^{-1} +a^{10} z^2-2 a^8 z^2+6 a^6 z^2+a^4 z^2-3 a^2 z^2+22 z^2 a^{-2} +27 z^2-3 a^5 z-a^3 z+a z-z a^{-1} -a^6-3 a^{-2} -3 }[/math] |
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