K12n188
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^9+3 q^8-6 q^7+8 q^6-10 q^5+11 q^4-9 q^3+8 q^2-5 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+9 t^2-12 t+13-12 t^{-1} +9 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+5 z^4+4 z^2+1 }[/math] |
| Determinant | 65 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} +13 z^4 a^{-4} -4 z^4 a^{-6} -4 z^2 a^{-2} +13 z^2 a^{-4} -5 z^2 a^{-6} - a^{-2} +5 a^{-4} -3 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +3 z^9 a^{-3} +5 z^9 a^{-5} +2 z^9 a^{-7} +3 z^8 a^{-2} +3 z^8 a^{-4} +z^8 a^{-6} +z^8 a^{-8} +z^7 a^{-1} -10 z^7 a^{-3} -16 z^7 a^{-5} -5 z^7 a^{-7} -13 z^6 a^{-2} -24 z^6 a^{-4} -9 z^6 a^{-6} +2 z^6 a^{-8} -4 z^5 a^{-1} +4 z^5 a^{-3} +12 z^5 a^{-5} +10 z^5 a^{-7} +6 z^5 a^{-9} +16 z^4 a^{-2} +33 z^4 a^{-4} +11 z^4 a^{-6} -3 z^4 a^{-8} +3 z^4 a^{-10} +4 z^3 a^{-1} +6 z^3 a^{-3} -z^3 a^{-5} -11 z^3 a^{-7} -7 z^3 a^{-9} +z^3 a^{-11} -7 z^2 a^{-2} -18 z^2 a^{-4} -9 z^2 a^{-6} +z^2 a^{-8} -z^2 a^{-10} -z a^{-1} -2 z a^{-3} -2 z a^{-5} +2 z a^{-7} +3 z a^{-9} + a^{-2} +5 a^{-4} +3 a^{-6} }[/math] |
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