K13n3756
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Polynomial invariants
| Jones polynomial | Data:K13n3756/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+5 t^3-t^2-8 t+13-8 t^{-1} - t^{-2} +5 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13n3756/Conway Polynomial |
| Determinant | 13 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-4} -z^8 a^{-6} +z^6 a^{-2} -7 z^6 a^{-4} -6 z^6 a^{-6} +z^6 a^{-8} +6 z^4 a^{-2} -16 z^4 a^{-4} -8 z^4 a^{-6} +7 z^4 a^{-8} +10 z^2 a^{-2} -17 z^2 a^{-4} +10 z^2 a^{-8} -2 z^2 a^{-10} +5 a^{-2} -8 a^{-4} +3 a^{-6} +3 a^{-8} -2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +z^{10} a^{-2} +3 z^{10} a^{-4} +2 z^{10} a^{-6} -8 z^9 a^{-3} -7 z^9 a^{-5} +2 z^9 a^{-7} +z^9 a^{-9} -9 z^8 a^{-2} -26 z^8 a^{-4} -16 z^8 a^{-6} +3 z^8 a^{-8} +2 z^8 a^{-10} +21 z^7 a^{-3} +12 z^7 a^{-5} -15 z^7 a^{-7} -4 z^7 a^{-9} +2 z^7 a^{-11} +29 z^6 a^{-2} +77 z^6 a^{-4} +39 z^6 a^{-6} -20 z^6 a^{-8} -9 z^6 a^{-10} +2 z^6 a^{-12} -21 z^5 a^{-3} +30 z^5 a^{-7} +2 z^5 a^{-9} -6 z^5 a^{-11} +z^5 a^{-13} -41 z^4 a^{-2} -97 z^4 a^{-4} -38 z^4 a^{-6} +38 z^4 a^{-8} +14 z^4 a^{-10} -6 z^4 a^{-12} +7 z^3 a^{-3} -9 z^3 a^{-5} -17 z^3 a^{-7} +5 z^3 a^{-9} +3 z^3 a^{-11} -3 z^3 a^{-13} +25 z^2 a^{-2} +50 z^2 a^{-4} +17 z^2 a^{-6} -20 z^2 a^{-8} -10 z^2 a^{-10} +2 z^2 a^{-12} -z a^{-3} +z a^{-5} +3 z a^{-7} -z a^{-9} -z a^{-11} +z a^{-13} -5 a^{-2} -8 a^{-4} -3 a^{-6} +3 a^{-8} +2 a^{-10} }[/math] |
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