K12n41
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+3 q^3-3 q^2+3 q-3+2 q^{-1} - q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-4 t^2+4 t-1+4 t^{-1} -4 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+2 z^4-3 z^2+1 }[/math] |
| Determinant | 19 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6-a^2 z^4-2 z^4 a^{-2} +5 z^4-4 a^2 z^2-7 z^2 a^{-2} +z^2 a^{-4} +7 z^2+a^4-2 a^2-4 a^{-2} +2 a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+2 a z^9+4 z^9 a^{-1} +2 z^9 a^{-3} +a^2 z^8-3 z^8 a^{-2} +z^8 a^{-4} -3 z^8-12 a z^7-24 z^7 a^{-1} -12 z^7 a^{-3} -6 a^2 z^6-8 z^6 a^{-2} -6 z^6 a^{-4} -8 z^6+20 a z^5+41 z^5 a^{-1} +21 z^5 a^{-3} +9 a^2 z^4+27 z^4 a^{-2} +11 z^4 a^{-4} +25 z^4-2 a^3 z^3-13 a z^3-24 z^3 a^{-1} -13 z^3 a^{-3} -a^4 z^2-7 a^2 z^2-20 z^2 a^{-2} -8 z^2 a^{-4} -18 z^2+a^3 z+2 a z+4 z a^{-1} +3 z a^{-3} +a^4+2 a^2+4 a^{-2} +2 a^{-4} +4 }[/math] |
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