K12a589
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+4-9 q^{-1} +16 q^{-2} -22 q^{-3} +28 q^{-4} -29 q^{-5} +27 q^{-6} -22 q^{-7} +15 q^{-8} -8 q^{-9} +3 q^{-10} - q^{-11} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+23 t^2-37 t+43-37 t^{-1} +23 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+9 z^4+6 z^2+1 }[/math] |
| Determinant | 185 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^8-4 z^4 a^8-6 z^2 a^8-3 a^8+z^8 a^6+5 z^6 a^6+11 z^4 a^6+12 z^2 a^6+4 a^6+z^8 a^4+4 z^6 a^4+5 z^4 a^4+2 z^2 a^4-z^6 a^2-3 z^4 a^2-2 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^5 a^{13}-2 z^3 a^{13}+z a^{13}+3 z^6 a^{12}-4 z^4 a^{12}+z^2 a^{12}+6 z^7 a^{11}-8 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+9 z^8 a^{10}-15 z^6 a^{10}+15 z^4 a^{10}-6 z^2 a^{10}+9 z^9 a^9-12 z^7 a^9+6 z^5 a^9+2 z^3 a^9-z a^9+6 z^{10} a^8-z^8 a^8-12 z^6 a^8+9 z^4 a^8+4 z^2 a^8-3 a^8+2 z^{11} a^7+12 z^9 a^7-35 z^7 a^7+31 z^5 a^7-14 z^3 a^7+3 z a^7+12 z^{10} a^6-26 z^8 a^6+19 z^6 a^6-17 z^4 a^6+13 z^2 a^6-4 a^6+2 z^{11} a^5+10 z^9 a^5-40 z^7 a^5+39 z^5 a^5-17 z^3 a^5+2 z a^5+6 z^{10} a^4-12 z^8 a^4+5 z^4 a^4-z^2 a^4+7 z^9 a^3-22 z^7 a^3+20 z^5 a^3-6 z^3 a^3+z a^3+4 z^8 a^2-13 z^6 a^2+12 z^4 a^2-3 z^2 a^2+z^7 a-3 z^5 a+2 z^3 a }[/math] |
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