K12n316
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-3 q^{11}+5 q^{10}-8 q^9+10 q^8-11 q^7+10 q^6-8 q^5+6 q^4-2 q^3+q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+7 t^2-15 t+19-15 t^{-1} +7 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+z^4+4 z^2+1 }[/math] |
| Determinant | 65 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-8} +z^4 a^{-4} +3 z^4 a^{-6} -4 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-4} +7 z^2 a^{-6} -7 z^2 a^{-8} +2 z^2 a^{-10} + a^{-4} +3 a^{-6} -4 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-8} +z^{10} a^{-10} +z^9 a^{-7} +4 z^9 a^{-9} +3 z^9 a^{-11} -3 z^8 a^{-8} +z^8 a^{-10} +4 z^8 a^{-12} -3 z^7 a^{-7} -14 z^7 a^{-9} -8 z^7 a^{-11} +3 z^7 a^{-13} +4 z^6 a^{-6} +9 z^6 a^{-8} -9 z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} +2 z^5 a^{-5} +12 z^5 a^{-7} +24 z^5 a^{-9} +4 z^5 a^{-11} -10 z^5 a^{-13} +z^4 a^{-4} -7 z^4 a^{-6} -10 z^4 a^{-8} +11 z^4 a^{-10} +10 z^4 a^{-12} -3 z^4 a^{-14} -2 z^3 a^{-5} -14 z^3 a^{-7} -18 z^3 a^{-9} +z^3 a^{-11} +7 z^3 a^{-13} -2 z^2 a^{-4} +7 z^2 a^{-6} +9 z^2 a^{-8} -3 z^2 a^{-10} -2 z^2 a^{-12} +z^2 a^{-14} +5 z a^{-7} +5 z a^{-9} -z a^{-11} -z a^{-13} + a^{-4} -3 a^{-6} -4 a^{-8} - a^{-10} }[/math] |
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