K12a382
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^2-3 q+7-11 q^{-1} +16 q^{-2} -19 q^{-3} +20 q^{-4} -19 q^{-5} +16 q^{-6} -11 q^{-7} +6 q^{-8} -3 q^{-9} + q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+18 t^2-26 t+29-26 t^{-1} +18 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+z^6-4 z^4-z^2+1 }[/math] |
| Determinant | 133 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^8+3 z^2 a^8+a^8-2 z^6 a^6-8 z^4 a^6-9 z^2 a^6-3 a^6+z^8 a^4+5 z^6 a^4+10 z^4 a^4+11 z^2 a^4+4 a^4-2 z^6 a^2-8 z^4 a^2-9 z^2 a^2-3 a^2+z^4+3 z^2+2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^4 a^{12}-z^2 a^{12}+3 z^5 a^{11}-3 z^3 a^{11}+z a^{11}+5 z^6 a^{10}-4 z^4 a^{10}+z^2 a^{10}+7 z^7 a^9-7 z^5 a^9+z^3 a^9+z a^9+9 z^8 a^8-17 z^6 a^8+14 z^4 a^8-6 z^2 a^8+a^8+8 z^9 a^7-15 z^7 a^7+6 z^5 a^7-z^3 a^7+4 z^{10} a^6+4 z^8 a^6-42 z^6 a^6+51 z^4 a^6-22 z^2 a^6+3 a^6+z^{11} a^5+12 z^9 a^5-48 z^7 a^5+46 z^5 a^5-14 z^3 a^5+z a^5+7 z^{10} a^4-14 z^8 a^4-21 z^6 a^4+50 z^4 a^4-26 z^2 a^4+4 a^4+z^{11} a^3+7 z^9 a^3-40 z^7 a^3+51 z^5 a^3-20 z^3 a^3+2 z a^3+3 z^{10} a^2-8 z^8 a^2-6 z^6 a^2+27 z^4 a^2-19 z^2 a^2+3 a^2+3 z^9 a-14 z^7 a+21 z^5 a-11 z^3 a+z a+z^8-5 z^6+9 z^4-7 z^2+2 }[/math] |
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