K12n18
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-6 q^3+11 q^2-15 q+18-18 q^{-1} +16 q^{-2} -12 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+8 t^2-26 t+39-26 t^{-1} +8 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+2 z^4-3 z^2+1 }[/math] |
| Determinant | 109 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-3 z^2 a^4-2 a^4+3 z^4 a^2+4 z^2 a^2+2 a^2-z^6-2 z^4-3 z^2+z^4 a^{-2} -z^2 a^{-2} - a^{-2} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+3 a^3 z^9+6 a z^9+3 z^9 a^{-1} +4 a^4 z^8+8 a^2 z^8+3 z^8 a^{-2} +7 z^8+3 a^5 z^7+2 a^3 z^7-2 a z^7+z^7 a^{-3} +a^6 z^6-6 a^4 z^6-14 a^2 z^6-7 z^6-8 a^5 z^5-16 a^3 z^5-9 a z^5+4 z^5 a^{-1} +5 z^5 a^{-3} -3 a^6 z^4-3 a^4 z^4-3 a^2 z^4+2 z^4 a^{-2} +3 z^4 a^{-4} -4 z^4+7 a^5 z^3+12 a^3 z^3+2 a z^3-9 z^3 a^{-1} -6 z^3 a^{-3} +3 a^6 z^2+7 a^4 z^2+8 a^2 z^2-4 z^2 a^{-2} -3 z^2 a^{-4} +3 z^2-2 a^5 z-2 a^3 z+a z+3 z a^{-1} +2 z a^{-3} -a^6-2 a^4-2 a^2+ a^{-2} + a^{-4} }[/math] |
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