K12a673
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-9 q^6+17 q^5-25 q^4+30 q^3-32 q^2+30 q-24+17 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-25 t^2+43 t-49+43 t^{-1} -25 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+3 z^4-z^2+1 }[/math] |
| Determinant | 203 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-7 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-7 z^2 a^{-2} +5 z^2 a^{-4} -2 z^2 a^{-6} +5 z^2-2 a^{-2} + a^{-4} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +8 z^{10} a^{-4} +5 z^{10}+6 a z^9+12 z^9 a^{-1} +19 z^9 a^{-3} +13 z^9 a^{-5} +4 a^2 z^8-21 z^8 a^{-2} -3 z^8 a^{-4} +12 z^8 a^{-6} -2 z^8+a^3 z^7-14 a z^7-40 z^7 a^{-1} -57 z^7 a^{-3} -24 z^7 a^{-5} +8 z^7 a^{-7} -13 a^2 z^6-5 z^6 a^{-2} -17 z^6 a^{-4} -19 z^6 a^{-6} +4 z^6 a^{-8} -24 z^6-3 a^3 z^5+4 a z^5+29 z^5 a^{-1} +55 z^5 a^{-3} +22 z^5 a^{-5} -10 z^5 a^{-7} +z^5 a^{-9} +14 a^2 z^4+18 z^4 a^{-2} +21 z^4 a^{-4} +12 z^4 a^{-6} -5 z^4 a^{-8} +28 z^4+3 a^3 z^3+6 a z^3-7 z^3 a^{-1} -21 z^3 a^{-3} -7 z^3 a^{-5} +3 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2-11 z^2 a^{-2} -7 z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-8} -11 z^2-a^3 z-2 a z+z a^{-3} +2 a^{-2} + a^{-4} +2 }[/math] |
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