K12a1287
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-q^5+2 q^4-3 q^3+4 q^2-5 q+5-5 q^{-1} +4 q^{-2} -3 q^{-3} +2 q^{-4} - q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -9 t+19-9 t^{-1} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-9 z^2 }[/math] |
| Determinant | 37 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-z^2 a^4-2 z^2 a^2-3 z^2-1-2 z^2 a^{-2} -z^2 a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +a^2 z^{10}+z^{10} a^{-2} +2 z^{10}+a^3 z^9-8 a z^9-8 z^9 a^{-1} +z^9 a^{-3} +a^4 z^8-6 a^2 z^8-6 z^8 a^{-2} +z^8 a^{-4} -14 z^8+a^5 z^7-5 a^3 z^7+26 a z^7+26 z^7 a^{-1} -5 z^7 a^{-3} +z^7 a^{-5} +a^6 z^6-4 a^4 z^6+13 a^2 z^6+13 z^6 a^{-2} -4 z^6 a^{-4} +z^6 a^{-6} +36 z^6-4 a^5 z^5+9 a^3 z^5-41 a z^5-41 z^5 a^{-1} +9 z^5 a^{-3} -4 z^5 a^{-5} -5 a^6 z^4+4 a^4 z^4-10 a^2 z^4-10 z^4 a^{-2} +4 z^4 a^{-4} -5 z^4 a^{-6} -38 z^4+3 a^5 z^3-7 a^3 z^3+33 a z^3+33 z^3 a^{-1} -7 z^3 a^{-3} +3 z^3 a^{-5} +6 a^6 z^2-2 a^4 z^2+a^2 z^2+z^2 a^{-2} -2 z^2 a^{-4} +6 z^2 a^{-6} +18 z^2-9 a z-9 z a^{-1} -a^6- a^{-6} -1 }[/math] |
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