K12n405
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Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^9+3 q^8-6 q^7+9 q^6-11 q^5+12 q^4-11 q^3+9 q^2-6 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+13 t^2-12 t+9-12 t^{-1} +13 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+2 z^6-3 z^4+2 z^2+1 }[/math] |
| Determinant | 73 |
| 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} +8 z^4 a^{-4} -9 z^4 a^{-6} +z^4 a^{-8} +7 z^2 a^{-4} -10 z^2 a^{-6} +5 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} +9 z^9 a^{-5} +4 z^9 a^{-7} +4 z^8 a^{-2} -z^8 a^{-6} +3 z^8 a^{-8} +z^7 a^{-1} -20 z^7 a^{-3} -37 z^7 a^{-5} -15 z^7 a^{-7} +z^7 a^{-9} -16 z^6 a^{-2} -25 z^6 a^{-4} -19 z^6 a^{-6} -10 z^6 a^{-8} -3 z^5 a^{-1} +20 z^5 a^{-3} +45 z^5 a^{-5} +22 z^5 a^{-7} +15 z^4 a^{-2} +36 z^4 a^{-4} +36 z^4 a^{-6} +18 z^4 a^{-8} +3 z^4 a^{-10} +z^3 a^{-1} -6 z^3 a^{-3} -20 z^3 a^{-5} -13 z^3 a^{-7} +z^3 a^{-9} +z^3 a^{-11} -2 z^2 a^{-2} -15 z^2 a^{-4} -23 z^2 a^{-6} -13 z^2 a^{-8} -3 z^2 a^{-10} +z a^{-3} +2 z a^{-5} +2 z a^{-7} -z a^{-11} - a^{-2} +2 a^{-4} +4 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
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