K12n8
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^8-3 q^7+6 q^6-8 q^5+9 q^4-10 q^3+9 q^2-7 q+5-2 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+9 t^2-10 t+11-10 t^{-1} +9 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6-z^4-3 z^2+1 }[/math] |
| Determinant | 61 |
| 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} +13 z^4 a^{-4} -5 z^4 a^{-6} +z^4-15 z^2 a^{-2} +14 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +4 z^2-7 a^{-2} +6 a^{-4} -3 a^{-6} + a^{-8} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +2 z^9 a^{-1} +6 z^9 a^{-3} +4 z^9 a^{-5} +z^8 a^{-2} +6 z^8 a^{-4} +6 z^8 a^{-6} +z^8-10 z^7 a^{-1} -24 z^7 a^{-3} -10 z^7 a^{-5} +4 z^7 a^{-7} -23 z^6 a^{-2} -39 z^6 a^{-4} -21 z^6 a^{-6} +z^6 a^{-8} -6 z^6+15 z^5 a^{-1} +21 z^5 a^{-3} -4 z^5 a^{-5} -10 z^5 a^{-7} +46 z^4 a^{-2} +53 z^4 a^{-4} +22 z^4 a^{-6} +2 z^4 a^{-8} +13 z^4-6 z^3 a^{-1} +3 z^3 a^{-3} +13 z^3 a^{-5} +7 z^3 a^{-7} +3 z^3 a^{-9} -31 z^2 a^{-2} -27 z^2 a^{-4} -12 z^2 a^{-6} -3 z^2 a^{-8} +z^2 a^{-10} -12 z^2-z a^{-1} -5 z a^{-3} -5 z a^{-5} -2 z a^{-7} -z a^{-9} +7 a^{-2} +6 a^{-4} +3 a^{-6} + a^{-8} +4 }[/math] |
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