K12n831
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-4 q^8+8 q^7-12 q^6+15 q^5-17 q^4+16 q^3-12 q^2+9 q-4+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-12 t^2+20 t-23+20 t^{-1} -12 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-2 z^4+z^2+1 }[/math] |
| Determinant | 99 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-4} +z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +3 z^4 a^{-2} -8 z^4 a^{-4} +3 z^4 a^{-6} +3 z^2 a^{-2} -4 z^2 a^{-4} +2 z^2 a^{-6} +2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-3} +5 z^9 a^{-5} +4 z^9 a^{-7} +2 z^8 a^{-4} +8 z^8 a^{-6} +6 z^8 a^{-8} +5 z^7 a^{-3} -z^7 a^{-5} -2 z^7 a^{-7} +4 z^7 a^{-9} +9 z^6 a^{-2} +6 z^6 a^{-4} -18 z^6 a^{-6} -14 z^6 a^{-8} +z^6 a^{-10} +4 z^5 a^{-1} -5 z^5 a^{-3} -13 z^5 a^{-5} -14 z^5 a^{-7} -10 z^5 a^{-9} -11 z^4 a^{-2} -16 z^4 a^{-4} +4 z^4 a^{-6} +6 z^4 a^{-8} -2 z^4 a^{-10} +z^4-2 z^3 a^{-1} +2 z^3 a^{-3} +11 z^3 a^{-5} +13 z^3 a^{-7} +6 z^3 a^{-9} +5 z^2 a^{-2} +8 z^2 a^{-4} +3 z^2 a^{-6} +z^2 a^{-8} +z^2 a^{-10} -2 z a^{-5} -3 z a^{-7} -z a^{-9} -2 a^{-2} - a^{-4} }[/math] |
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