K12a469
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+4 q^6-10 q^5+18 q^4-26 q^3+32 q^2-34 q+33-26 q^{-1} +18 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+24 t^2-47 t+59-47 t^{-1} +24 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6+2 z^4+2 z^2+1 }[/math] |
| Determinant | 217 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-3 z^6 a^{-2} +5 z^6-3 a^2 z^4-10 z^4 a^{-2} +3 z^4 a^{-4} +12 z^4-4 a^2 z^2-12 z^2 a^{-2} +6 z^2 a^{-4} -z^2 a^{-6} +13 z^2-2 a^2-5 a^{-2} +3 a^{-4} - a^{-6} +6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +14 z^{10} a^{-2} +6 z^{10} a^{-4} +8 z^{10}+14 a z^9+24 z^9 a^{-1} +17 z^9 a^{-3} +7 z^9 a^{-5} +14 a^2 z^8-15 z^8 a^{-2} -4 z^8 a^{-4} +4 z^8 a^{-6} +7 z^8+9 a^3 z^7-21 a z^7-69 z^7 a^{-1} -58 z^7 a^{-3} -18 z^7 a^{-5} +z^7 a^{-7} +4 a^4 z^6-25 a^2 z^6-36 z^6 a^{-2} -25 z^6 a^{-4} -12 z^6 a^{-6} -52 z^6+a^5 z^5-12 a^3 z^5+9 a z^5+59 z^5 a^{-1} +52 z^5 a^{-3} +12 z^5 a^{-5} -3 z^5 a^{-7} -4 a^4 z^4+23 a^2 z^4+60 z^4 a^{-2} +34 z^4 a^{-4} +12 z^4 a^{-6} +65 z^4-a^5 z^3+6 a^3 z^3+5 a z^3-16 z^3 a^{-1} -19 z^3 a^{-3} -2 z^3 a^{-5} +3 z^3 a^{-7} -11 a^2 z^2-31 z^2 a^{-2} -17 z^2 a^{-4} -5 z^2 a^{-6} -30 z^2-2 a^3 z-3 a z+2 z a^{-3} -z a^{-7} +2 a^2+5 a^{-2} +3 a^{-4} + a^{-6} +6 }[/math] |
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