K12n409
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{-1} -3 q^{-2} +5 q^{-3} -5 q^{-4} +7 q^{-5} -6 q^{-6} +5 q^{-7} -4 q^{-8} +2 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-3 t^2+9 t-13+9 t^{-1} -3 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+3 z^4+6 z^2+1 }[/math] |
| Determinant | 39 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-3 z^2 a^8-3 a^8+z^6 a^6+5 z^4 a^6+9 z^2 a^6+4 a^6-z^4 a^4-z^2 a^4+z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-5 z^5 a^{11}+7 z^3 a^{11}-3 z a^{11}+2 z^8 a^{10}-9 z^6 a^{10}+10 z^4 a^{10}-2 z^2 a^{10}+2 z^9 a^9-8 z^7 a^9+7 z^5 a^9-2 z^3 a^9+2 z a^9+z^{10} a^8-3 z^8 a^8+2 z^6 a^8-6 z^4 a^8+8 z^2 a^8-3 a^8+3 z^9 a^7-14 z^7 a^7+24 z^5 a^7-23 z^3 a^7+8 z a^7+z^{10} a^6-5 z^8 a^6+12 z^6 a^6-16 z^4 a^6+9 z^2 a^6-4 a^6+z^9 a^5-5 z^7 a^5+12 z^5 a^5-12 z^3 a^5+4 z a^5+z^6 a^4+2 z^3 a^3+z a^3+z^2 a^2 }[/math] |
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