K12n527
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+8 q^8-12 q^7+15 q^6-16 q^5+14 q^4-11 q^3+8 q^2-3 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+12 t^2-20 t+23-20 t^{-1} +12 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-6 z^4+z^2+1 }[/math] |
| Determinant | 93 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} +z^4 a^{-2} -z^4 a^{-4} -8 z^4 a^{-6} +2 z^4 a^{-8} +2 z^2 a^{-2} +4 z^2 a^{-4} -11 z^2 a^{-6} +6 z^2 a^{-8} + a^{-2} +3 a^{-4} -6 a^{-6} +4 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +4 z^9 a^{-5} +6 z^9 a^{-7} +2 z^9 a^{-9} +5 z^8 a^{-4} +9 z^8 a^{-6} +5 z^8 a^{-8} +z^8 a^{-10} +3 z^7 a^{-3} -5 z^7 a^{-5} -9 z^7 a^{-7} -z^7 a^{-9} +z^6 a^{-2} -12 z^6 a^{-4} -33 z^6 a^{-6} -18 z^6 a^{-8} +2 z^6 a^{-10} -7 z^5 a^{-3} -7 z^5 a^{-5} -5 z^5 a^{-7} -z^5 a^{-9} +4 z^5 a^{-11} -3 z^4 a^{-2} +8 z^4 a^{-4} +40 z^4 a^{-6} +28 z^4 a^{-8} +z^4 a^{-12} +3 z^3 a^{-3} +8 z^3 a^{-5} +17 z^3 a^{-7} +8 z^3 a^{-9} -4 z^3 a^{-11} +3 z^2 a^{-2} -8 z^2 a^{-4} -25 z^2 a^{-6} -16 z^2 a^{-8} -3 z^2 a^{-10} -z^2 a^{-12} -3 z a^{-5} -6 z a^{-7} -4 z a^{-9} -z a^{-11} - a^{-2} +3 a^{-4} +6 a^{-6} +4 a^{-8} + a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
