K12n543
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^{-1} -5 q^{-2} +8 q^{-3} -9 q^{-4} +11 q^{-5} -10 q^{-6} +8 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-5 t^2+15 t-21+15 t^{-1} -5 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+z^4+4 z^2+1 }[/math] |
| Determinant | 63 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^8-2 z^2 a^8-2 a^8+z^6 a^6+4 z^4 a^6+7 z^2 a^6+3 a^6-2 z^4 a^4-3 z^2 a^4-a^4+2 z^2 a^2+a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^7 a^{11}-4 z^5 a^{11}+5 z^3 a^{11}-2 z a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+13 z^4 a^{10}-3 z^2 a^{10}+3 z^9 a^9-9 z^7 a^9+2 z^5 a^9+6 z^3 a^9-z a^9+z^{10} a^8+2 z^8 a^8-14 z^6 a^8+8 z^4 a^8+3 z^2 a^8-2 a^8+4 z^9 a^7-9 z^7 a^7-z^5 a^7+4 z^3 a^7-z a^7+z^{10} a^6-z^8 a^6+3 z^6 a^6-13 z^4 a^6+9 z^2 a^6-3 a^6+z^9 a^5+z^7 a^5-6 z^5 a^5+7 z^3 a^5-3 z a^5+5 z^6 a^4-8 z^4 a^4+6 z^2 a^4-a^4+z^5 a^3+4 z^3 a^3-z a^3+3 z^2 a^2-a^2 }[/math] |
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