K12a269
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+8 q^{10}-14 q^9+20 q^8-23 q^7+24 q^6-22 q^5+17 q^4-11 q^3+6 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+18 t^2-34 t+41-34 t^{-1} +18 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -4 z^6-6 z^4+2 z^2+1 }[/math] |
| Determinant | 153 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -2 z^4 a^{-4} -5 z^4 a^{-6} -z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} -z^2 a^{-4} -3 z^2 a^{-6} +2 z^2 a^{-8} +z^2 a^{-10} +2 a^{-2} - a^{-4} - a^{-6} +2 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +4 z^9 a^{-5} +8 z^9 a^{-7} +11 z^9 a^{-9} +7 z^9 a^{-11} +3 z^8 a^{-4} -2 z^8 a^{-6} -11 z^8 a^{-8} +z^8 a^{-10} +7 z^8 a^{-12} +2 z^7 a^{-3} -9 z^7 a^{-5} -28 z^7 a^{-7} -35 z^7 a^{-9} -14 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-2} -5 z^6 a^{-4} -4 z^6 a^{-6} -z^6 a^{-8} -22 z^6 a^{-10} -18 z^6 a^{-12} +z^6 a^{-14} -5 z^5 a^{-3} +13 z^5 a^{-5} +46 z^5 a^{-7} +43 z^5 a^{-9} +5 z^5 a^{-11} -10 z^5 a^{-13} -4 z^4 a^{-2} -z^4 a^{-4} +11 z^4 a^{-6} +22 z^4 a^{-8} +29 z^4 a^{-10} +13 z^4 a^{-12} -2 z^4 a^{-14} +2 z^3 a^{-3} -14 z^3 a^{-5} -34 z^3 a^{-7} -22 z^3 a^{-9} +z^3 a^{-11} +5 z^3 a^{-13} +5 z^2 a^{-2} +3 z^2 a^{-4} -9 z^2 a^{-6} -16 z^2 a^{-8} -13 z^2 a^{-10} -4 z^2 a^{-12} +z a^{-3} +5 z a^{-5} +9 z a^{-7} +5 z a^{-9} -2 a^{-2} - a^{-4} + a^{-6} +2 a^{-8} + a^{-10} }[/math] |
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