K12n459
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^9+6 q^8-10 q^7+14 q^6-17 q^5+17 q^4-15 q^3+12 q^2-7 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+15 t^2-20 t+21-20 t^{-1} +15 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^6-z^4+2 z^2+1 }[/math] |
| Determinant | 105 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -2 z^6 a^{-6} -3 z^4 a^{-2} +9 z^4 a^{-4} -8 z^4 a^{-6} +z^4 a^{-8} -z^2 a^{-2} +8 z^2 a^{-4} -9 z^2 a^{-6} +4 z^2 a^{-8} + a^{-2} +2 a^{-4} -4 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-3} +11 z^9 a^{-5} +6 z^9 a^{-7} +4 z^8 a^{-2} +5 z^8 a^{-4} +8 z^8 a^{-6} +7 z^8 a^{-8} +z^7 a^{-1} -16 z^7 a^{-3} -33 z^7 a^{-5} -12 z^7 a^{-7} +4 z^7 a^{-9} -15 z^6 a^{-2} -36 z^6 a^{-4} -37 z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -3 z^5 a^{-1} +12 z^5 a^{-3} +29 z^5 a^{-5} +13 z^5 a^{-7} -z^5 a^{-9} +16 z^4 a^{-2} +43 z^4 a^{-4} +42 z^4 a^{-6} +21 z^4 a^{-8} +6 z^4 a^{-10} +2 z^3 a^{-1} -2 z^3 a^{-3} -15 z^3 a^{-5} -14 z^3 a^{-7} +3 z^3 a^{-11} -4 z^2 a^{-2} -17 z^2 a^{-4} -23 z^2 a^{-6} -15 z^2 a^{-8} -5 z^2 a^{-10} +2 z a^{-3} +5 z a^{-5} +5 z a^{-7} +z a^{-9} -z a^{-11} - a^{-2} +2 a^{-4} +4 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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