K12n221
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+2 q^6-3 q^5+4 q^4-3 q^3+2 q^2-q+2 q^{-1} -2 q^{-2} +2 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^2-2 t+3-2 t^{-1} + t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^4+2 z^2+1 }[/math] |
| Determinant | 9 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} +z^6-a^2 z^4-6 z^4 a^{-2} +2 z^4 a^{-4} +6 z^4-3 a^2 z^2-12 z^2 a^{-2} +7 z^2 a^{-4} -z^2 a^{-6} +11 z^2-2 a^2-8 a^{-2} +6 a^{-4} -2 a^{-6} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^9+z^9 a^{-1} +z^9 a^{-3} +z^9 a^{-5} +2 a^2 z^8+3 z^8 a^{-2} +4 z^8 a^{-4} +2 z^8 a^{-6} +3 z^8+a^3 z^7-4 a z^7-6 z^7 a^{-1} -4 z^7 a^{-3} -2 z^7 a^{-5} +z^7 a^{-7} -11 a^2 z^6-22 z^6 a^{-2} -22 z^6 a^{-4} -10 z^6 a^{-6} -21 z^6-5 a^3 z^5-2 a z^5+4 z^5 a^{-1} -2 z^5 a^{-3} -8 z^5 a^{-5} -5 z^5 a^{-7} +16 a^2 z^4+43 z^4 a^{-2} +34 z^4 a^{-4} +14 z^4 a^{-6} +39 z^4+6 a^3 z^3+10 a z^3+5 z^3 a^{-1} +8 z^3 a^{-3} +14 z^3 a^{-5} +7 z^3 a^{-7} -9 a^2 z^2-33 z^2 a^{-2} -23 z^2 a^{-4} -8 z^2 a^{-6} -27 z^2-2 a^3 z-4 a z-3 z a^{-1} -3 z a^{-3} -5 z a^{-5} -3 z a^{-7} +2 a^2+8 a^{-2} +6 a^{-4} +2 a^{-6} +7 }[/math] |
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