K12n429
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 3 q^{-1} -6 q^{-2} +9 q^{-3} -11 q^{-4} +12 q^{-5} -11 q^{-6} +9 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^2+18 t-27+18 t^{-1} -4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^4+2 z^2+1 }[/math] |
| Determinant | 71 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^{10}+3 z^2 a^8+2 a^8-2 z^4 a^6-2 z^2 a^6-a^6-2 z^4 a^4-2 z^2 a^4-a^4+3 z^2 a^2+2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+4 z^3 a^{11}-z a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+13 z^4 a^{10}-5 z^2 a^{10}+a^{10}+4 z^9 a^9-15 z^7 a^9+14 z^5 a^9-5 z^3 a^9+2 z a^9+2 z^{10} a^8-2 z^8 a^8-14 z^6 a^8+21 z^4 a^8-11 z^2 a^8+2 a^8+8 z^9 a^7-32 z^7 a^7+42 z^5 a^7-27 z^3 a^7+6 z a^7+2 z^{10} a^6-3 z^8 a^6-6 z^6 a^6+12 z^4 a^6-8 z^2 a^6+a^6+4 z^9 a^5-16 z^7 a^5+27 z^5 a^5-19 z^3 a^5+4 z a^5+2 z^8 a^4-4 z^6 a^4+4 z^4 a^4+2 z^2 a^4-a^4+3 z^5 a^3-z^3 a^3+z a^3+4 z^2 a^2-2 a^2 }[/math] |
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