K13n4031
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Polynomial invariants
| Jones polynomial | Data:K13n4031/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+15 t^2-21 t+23-21 t^{-1} +15 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13n4031/Conway Polynomial |
| Determinant | 109 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +4 z^6 a^{-4} -z^6 a^{-6} -2 z^4 a^{-2} +3 z^4 a^{-4} -2 z^4 a^{-6} +2 z^2 a^{-2} -3 z^2 a^{-4} +2 z^2 a^{-6} +3 a^{-2} -4 a^{-4} +3 a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-4} +3 z^{10} a^{-6} +7 z^9 a^{-3} +13 z^9 a^{-5} +6 z^9 a^{-7} +5 z^8 a^{-2} +2 z^8 a^{-4} +z^8 a^{-6} +4 z^8 a^{-8} +z^7 a^{-1} -22 z^7 a^{-3} -38 z^7 a^{-5} -14 z^7 a^{-7} +z^7 a^{-9} -16 z^6 a^{-2} -27 z^6 a^{-4} -15 z^6 a^{-6} -4 z^6 a^{-8} -2 z^5 a^{-1} +16 z^5 a^{-3} +29 z^5 a^{-5} +16 z^5 a^{-7} +5 z^5 a^{-9} +12 z^4 a^{-2} +17 z^4 a^{-4} +4 z^4 a^{-6} +3 z^4 a^{-8} +4 z^4 a^{-10} +z^3 a^{-1} -2 z^3 a^{-3} -12 z^3 a^{-5} -13 z^3 a^{-7} -3 z^3 a^{-9} +z^3 a^{-11} +3 z^2 a^{-2} +7 z^2 a^{-4} +6 z^2 a^{-6} +z^2 a^{-8} -z^2 a^{-10} +z a^{-3} +3 z a^{-5} +4 z a^{-7} +2 z a^{-9} -3 a^{-2} -4 a^{-4} -3 a^{-6} - a^{-8} }[/math] |
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