K12n592
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q+3-4 q^{-1} +6 q^{-2} -7 q^{-3} +8 q^{-4} -7 q^{-5} +6 q^{-6} -4 q^{-7} +2 q^{-8} - q^{-9} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+8 t^2-8 t+7-8 t^{-1} +8 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+4 z^4+4 z^2+1 }[/math] |
| Determinant | 49 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -a^8-z^6 a^6-4 z^4 a^6-3 z^2 a^6+z^8 a^4+6 z^6 a^4+12 z^4 a^4+10 z^2 a^4+2 a^4-z^6 a^2-4 z^4 a^2-3 z^2 a^2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^3 a^{11}-z a^{11}+2 z^4 a^{10}-z^2 a^{10}+3 z^5 a^9-3 z^3 a^9+2 z a^9+4 z^6 a^8-7 z^4 a^8+5 z^2 a^8-a^8+z^9 a^7-3 z^7 a^7+8 z^5 a^7-11 z^3 a^7+4 z a^7+z^{10} a^6-3 z^8 a^6+4 z^6 a^6-4 z^4 a^6+4 z^9 a^5-17 z^7 a^5+23 z^5 a^5-14 z^3 a^5+2 z a^5+z^{10} a^4-14 z^6 a^4+22 z^4 a^4-11 z^2 a^4+2 a^4+3 z^9 a^3-13 z^7 a^3+14 z^5 a^3-4 z^3 a^3+z a^3+3 z^8 a^2-14 z^6 a^2+17 z^4 a^2-5 z^2 a^2+z^7 a-4 z^5 a+3 z^3 a }[/math] |
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