K13a1219
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Polynomial invariants
| Jones polynomial | Data:K13a1219/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -6 t^3+32 t^2-72 t+93-72 t^{-1} +32 t^{-2} -6 t^{-3} }[/math] |
| Conway polynomial | Data:K13a1219/Conway Polynomial |
| Determinant | 313 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -2 z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -6 z^4 a^{-6} -3 z^4 a^{-8} +3 z^4 a^{-10} +z^2 a^{-2} +5 z^2 a^{-4} -4 z^2 a^{-6} -3 z^2 a^{-8} +4 z^2 a^{-10} -z^2 a^{-12} +3 a^{-4} - a^{-6} -2 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{12} a^{-8} +z^{12} a^{-10} +5 z^{11} a^{-7} +10 z^{11} a^{-9} +5 z^{11} a^{-11} +10 z^{10} a^{-6} +24 z^{10} a^{-8} +24 z^{10} a^{-10} +10 z^{10} a^{-12} +12 z^9 a^{-5} +18 z^9 a^{-7} +10 z^9 a^{-9} +14 z^9 a^{-11} +10 z^9 a^{-13} +9 z^8 a^{-4} -3 z^8 a^{-6} -51 z^8 a^{-8} -63 z^8 a^{-10} -19 z^8 a^{-12} +5 z^8 a^{-14} +4 z^7 a^{-3} -20 z^7 a^{-5} -59 z^7 a^{-7} -79 z^7 a^{-9} -75 z^7 a^{-11} -30 z^7 a^{-13} +z^7 a^{-15} +z^6 a^{-2} -18 z^6 a^{-4} -24 z^6 a^{-6} +33 z^6 a^{-8} +50 z^6 a^{-10} -2 z^6 a^{-12} -14 z^6 a^{-14} -7 z^5 a^{-3} +13 z^5 a^{-5} +61 z^5 a^{-7} +106 z^5 a^{-9} +95 z^5 a^{-11} +28 z^5 a^{-13} -2 z^5 a^{-15} -2 z^4 a^{-2} +16 z^4 a^{-4} +30 z^4 a^{-6} -6 z^4 a^{-8} -11 z^4 a^{-10} +16 z^4 a^{-12} +9 z^4 a^{-14} +3 z^3 a^{-3} -5 z^3 a^{-5} -31 z^3 a^{-7} -60 z^3 a^{-9} -46 z^3 a^{-11} -9 z^3 a^{-13} +z^2 a^{-2} -10 z^2 a^{-4} -13 z^2 a^{-6} +2 z^2 a^{-8} -z^2 a^{-10} -5 z^2 a^{-12} +8 z a^{-7} +14 z a^{-9} +6 z a^{-11} +3 a^{-4} + a^{-6} -2 a^{-8} - a^{-10} }[/math] |
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