K13n19
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Polynomial invariants
| Jones polynomial | Data:K13n19/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-10 t^2+4 t+1+4 t^{-1} -10 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13n19/Conway Polynomial |
| Determinant | 47 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -5 z^6 a^{-6} -5 z^6 a^{-8} +z^6 a^{-10} +5 z^4 a^{-4} -7 z^4 a^{-6} -6 z^4 a^{-8} +6 z^4 a^{-10} +7 z^2 a^{-4} -5 z^2 a^{-6} -3 z^2 a^{-8} +7 z^2 a^{-10} -2 z^2 a^{-12} +3 a^{-4} -2 a^{-6} - a^{-8} +2 a^{-10} - a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +2 z^9 a^{-5} +3 z^9 a^{-11} +z^9 a^{-13} +z^8 a^{-4} -7 z^8 a^{-6} -24 z^8 a^{-8} -17 z^8 a^{-10} +z^8 a^{-12} +2 z^8 a^{-14} -10 z^7 a^{-5} -17 z^7 a^{-7} -20 z^7 a^{-9} -21 z^7 a^{-11} -7 z^7 a^{-13} +z^7 a^{-15} -6 z^6 a^{-4} -z^6 a^{-6} +31 z^6 a^{-8} +27 z^6 a^{-10} -11 z^6 a^{-12} -12 z^6 a^{-14} +14 z^5 a^{-5} +28 z^5 a^{-7} +38 z^5 a^{-9} +39 z^5 a^{-11} +10 z^5 a^{-13} -5 z^5 a^{-15} +12 z^4 a^{-4} +15 z^4 a^{-6} -17 z^4 a^{-8} -19 z^4 a^{-10} +18 z^4 a^{-12} +17 z^4 a^{-14} -6 z^3 a^{-5} -16 z^3 a^{-7} -27 z^3 a^{-9} -26 z^3 a^{-11} -4 z^3 a^{-13} +5 z^3 a^{-15} -10 z^2 a^{-4} -11 z^2 a^{-6} +5 z^2 a^{-8} +7 z^2 a^{-10} -5 z^2 a^{-12} -6 z^2 a^{-14} +4 z a^{-7} +7 z a^{-9} +5 z a^{-11} +z a^{-13} -z a^{-15} +3 a^{-4} +2 a^{-6} - a^{-8} -2 a^{-10} - a^{-12} }[/math] |
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