K12a590
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+9 q^{11}-15 q^{10}+20 q^9-23 q^8+23 q^7-21 q^6+16 q^5-10 q^4+6 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-19 t^2+29 t-33+29 t^{-1} -19 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-5 z^4+2 z^2+1 }[/math] |
| Determinant | 151 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -4 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -9 z^4 a^{-6} -4 z^4 a^{-8} +3 z^4 a^{-10} +8 z^2 a^{-4} -8 z^2 a^{-6} +2 z^2 a^{-10} +4 a^{-4} -4 a^{-6} + a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +7 z^{10} a^{-8} +5 z^{10} a^{-10} +2 z^9 a^{-5} +4 z^9 a^{-7} +13 z^9 a^{-9} +11 z^9 a^{-11} +z^8 a^{-4} -4 z^8 a^{-6} -16 z^8 a^{-8} +4 z^8 a^{-10} +15 z^8 a^{-12} -9 z^7 a^{-5} -24 z^7 a^{-7} -43 z^7 a^{-9} -14 z^7 a^{-11} +14 z^7 a^{-13} -6 z^6 a^{-4} -9 z^6 a^{-6} -2 z^6 a^{-8} -32 z^6 a^{-10} -24 z^6 a^{-12} +9 z^6 a^{-14} +12 z^5 a^{-5} +28 z^5 a^{-7} +34 z^5 a^{-9} -5 z^5 a^{-11} -19 z^5 a^{-13} +4 z^5 a^{-15} +13 z^4 a^{-4} +26 z^4 a^{-6} +17 z^4 a^{-8} +22 z^4 a^{-10} +10 z^4 a^{-12} -7 z^4 a^{-14} +z^4 a^{-16} -3 z^3 a^{-5} -7 z^3 a^{-7} -9 z^3 a^{-9} +5 z^3 a^{-11} +9 z^3 a^{-13} -z^3 a^{-15} -12 z^2 a^{-4} -18 z^2 a^{-6} -7 z^2 a^{-8} -4 z^2 a^{-10} -z^2 a^{-12} +2 z^2 a^{-14} -2 z a^{-5} -z a^{-7} +z a^{-9} -z a^{-11} -z a^{-13} +4 a^{-4} +4 a^{-6} + a^{-8} }[/math] |
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