K12n16
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+q^7-q^5+3 q^4-4 q^3+5 q^2-5 q+4-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+7 t^2-5+7 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6-3 z^4-z^2+1 }[/math] |
| Determinant | 21 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -10 z^4 a^{-2} +12 z^4 a^{-4} -6 z^4 a^{-6} +z^4-13 z^2 a^{-2} +14 z^2 a^{-4} -8 z^2 a^{-6} +2 z^2 a^{-8} +4 z^2-6 a^{-2} +7 a^{-4} -4 a^{-6} + a^{-8} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +2 z^9 a^{-1} +5 z^9 a^{-3} +3 z^9 a^{-5} -z^8 a^{-2} +3 z^8 a^{-6} +z^8 a^{-8} +z^8-11 z^7 a^{-1} -27 z^7 a^{-3} -17 z^7 a^{-5} +z^7 a^{-7} +2 z^7 a^{-9} -17 z^6 a^{-2} -25 z^6 a^{-4} -21 z^6 a^{-6} -6 z^6 a^{-8} +z^6 a^{-10} -6 z^6+18 z^5 a^{-1} +39 z^5 a^{-3} +21 z^5 a^{-5} -10 z^5 a^{-7} -10 z^5 a^{-9} +39 z^4 a^{-2} +51 z^4 a^{-4} +35 z^4 a^{-6} +7 z^4 a^{-8} -4 z^4 a^{-10} +12 z^4-11 z^3 a^{-1} -19 z^3 a^{-3} -5 z^3 a^{-5} +13 z^3 a^{-7} +10 z^3 a^{-9} -28 z^2 a^{-2} -33 z^2 a^{-4} -21 z^2 a^{-6} -4 z^2 a^{-8} +2 z^2 a^{-10} -10 z^2+2 z a^{-1} +3 z a^{-3} -z a^{-5} -4 z a^{-7} -2 z a^{-9} +6 a^{-2} +7 a^{-4} +4 a^{-6} + a^{-8} +3 }[/math] |
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