K12n522
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{-1} -2 q^{-2} +3 q^{-3} -3 q^{-4} +4 q^{-5} -3 q^{-6} +3 q^{-7} -2 q^{-8} + q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-2 t^2+5 t-7+5 t^{-1} -2 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+4 z^4+6 z^2+1 }[/math] |
| Determinant | 23 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-4 z^2 a^8-4 a^8+z^6 a^6+6 z^4 a^6+12 z^2 a^6+7 a^6-z^4 a^4-3 z^2 a^4-3 a^4+z^2 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-6 z^5 a^{11}+10 z^3 a^{11}-4 z a^{11}+z^8 a^{10}-5 z^6 a^{10}+6 z^4 a^{10}-z^2 a^{10}+z^9 a^9-5 z^7 a^9+7 z^5 a^9-4 z^3 a^9+z a^9+z^{10} a^8-7 z^8 a^8+20 z^6 a^8-30 z^4 a^8+19 z^2 a^8-4 a^8+2 z^9 a^7-13 z^7 a^7+31 z^5 a^7-32 z^3 a^7+9 z a^7+z^{10} a^6-8 z^8 a^6+26 z^6 a^6-40 z^4 a^6+27 z^2 a^6-7 a^6+z^9 a^5-7 z^7 a^5+18 z^5 a^5-17 z^3 a^5+5 z a^5+z^6 a^4-4 z^4 a^4+8 z^2 a^4-3 a^4+z^3 a^3+z a^3+z^2 a^2-a^2 }[/math] |
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