K12a646
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-9 q^5+15 q^4-21 q^3+25 q^2-26 q+25-19 q^{-1} +13 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+21 t^2-33 t+39-33 t^{-1} +21 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+7 z^6+7 z^4+2 z^2+1 }[/math] |
| Determinant | 169 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +z^8-a^2 z^6+4 z^6 a^{-2} -z^6 a^{-4} +5 z^6-4 a^2 z^4+4 z^4 a^{-2} -3 z^4 a^{-4} +10 z^4-5 a^2 z^2-z^2 a^{-2} -2 z^2 a^{-4} +10 z^2-2 a^2-2 a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +11 z^{10} a^{-2} +6 z^{10} a^{-4} +5 z^{10}+7 a z^9+8 z^9 a^{-1} +8 z^9 a^{-3} +7 z^9 a^{-5} +7 a^2 z^8-26 z^8 a^{-2} -14 z^8 a^{-4} +4 z^8 a^{-6} -z^8+5 a^3 z^7-9 a z^7-27 z^7 a^{-1} -37 z^7 a^{-3} -23 z^7 a^{-5} +z^7 a^{-7} +3 a^4 z^6-11 a^2 z^6+14 z^6 a^{-2} +4 z^6 a^{-4} -13 z^6 a^{-6} -17 z^6+a^5 z^5-6 a^3 z^5+3 a z^5+21 z^5 a^{-1} +36 z^5 a^{-3} +22 z^5 a^{-5} -3 z^5 a^{-7} -5 a^4 z^4+11 a^2 z^4+4 z^4 a^{-2} +z^4 a^{-4} +11 z^4 a^{-6} +30 z^4-2 a^5 z^3+a^3 z^3+5 a z^3+z^3 a^{-1} -12 z^3 a^{-3} -9 z^3 a^{-5} +2 z^3 a^{-7} +2 a^4 z^2-8 a^2 z^2-6 z^2 a^{-2} -2 z^2 a^{-6} -18 z^2+a^5 z-3 a z-3 z a^{-1} +z a^{-5} +2 a^2+2 a^{-2} +5 }[/math] |
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