K12n198
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+2 q^3-2 q^2+4 q-4+4 q^{-1} -4 q^{-2} +3 q^{-3} -2 q^{-4} + q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-4 t^2+6 t-5+6 t^{-1} -4 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6+2 z^4-z^2+1 }[/math] |
| Determinant | 27 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6-2 a^2 z^4-z^4 a^{-2} +5 z^4+a^4 z^2-7 a^2 z^2-3 z^2 a^{-2} +8 z^2+2 a^4-5 a^2- a^{-2} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+2 a^3 z^9+5 a z^9+3 z^9 a^{-1} +a^4 z^8-2 a^2 z^8+3 z^8 a^{-2} -12 a^3 z^7-29 a z^7-16 z^7 a^{-1} +z^7 a^{-3} -6 a^4 z^6-13 a^2 z^6-17 z^6 a^{-2} -24 z^6+22 a^3 z^5+49 a z^5+22 z^5 a^{-1} -5 z^5 a^{-3} +11 a^4 z^4+35 a^2 z^4+26 z^4 a^{-2} +50 z^4-16 a^3 z^3-31 a z^3-11 z^3 a^{-1} +4 z^3 a^{-3} -8 a^4 z^2-26 a^2 z^2-14 z^2 a^{-2} -z^2 a^{-4} -31 z^2+4 a^3 z+7 a z+3 z a^{-1} +2 a^4+5 a^2+ a^{-2} +5 }[/math] |
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