K12n268
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-2 q^4+2 q^3-2 q^2+q+2-2 q^{-1} +3 q^{-2} -4 q^{-3} +3 q^{-4} -2 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t+5-2 t^{-1} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-2 z^2 }[/math] |
| Determinant | 9 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^6-2 z^2 a^4-2 a^4+z^4 a^2+2 z^2 a^2+a^2+2-z^4 a^{-2} -3 z^2 a^{-2} -2 a^{-2} +z^2 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+a z^9+3 z^9 a^{-1} +2 z^9 a^{-3} +a^4 z^8-5 z^8 a^{-2} +z^8 a^{-4} -7 z^8+2 a^5 z^7+3 a^3 z^7-8 a z^7-22 z^7 a^{-1} -13 z^7 a^{-3} +a^6 z^6-a^4 z^6+2 a^2 z^6+2 z^6 a^{-2} -6 z^6 a^{-4} +12 z^6-8 a^5 z^5-12 a^3 z^5+17 a z^5+46 z^5 a^{-1} +25 z^5 a^{-3} -4 a^6 z^4-8 a^4 z^4-10 a^2 z^4+10 z^4 a^{-2} +10 z^4 a^{-4} -6 z^4+8 a^5 z^3+11 a^3 z^3-13 a z^3-33 z^3 a^{-1} -17 z^3 a^{-3} +4 a^6 z^2+9 a^4 z^2+9 a^2 z^2-8 z^2 a^{-2} -5 z^2 a^{-4} +z^2-3 a^5 z-4 a^3 z+2 a z+6 z a^{-1} +3 z a^{-3} -a^6-2 a^4-a^2+2 a^{-2} + a^{-4} +2 }[/math] |
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