K12n866
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+7 q^4-13 q^3+19 q^2-23 q+24-21 q^{-1} +17 q^{-2} -10 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+15 t^2-30 t+39-30 t^{-1} +15 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+5 z^4+z^2+1 }[/math] |
| Determinant | 141 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +5 z^6-3 a^2 z^4-2 z^4 a^{-2} +10 z^4-4 a^2 z^2-2 z^2 a^{-2} -z^2 a^{-4} +8 z^2-a^2- a^{-2} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-2} +2 z^{10}+8 a z^9+11 z^9 a^{-1} +3 z^9 a^{-3} +12 a^2 z^8+6 z^8 a^{-2} +z^8 a^{-4} +17 z^8+9 a^3 z^7-2 a z^7-10 z^7 a^{-1} +z^7 a^{-3} +4 a^4 z^6-20 a^2 z^6-9 z^6 a^{-2} +6 z^6 a^{-4} -39 z^6+a^5 z^5-13 a^3 z^5-16 a z^5-10 z^5 a^{-1} -5 z^5 a^{-3} +3 z^5 a^{-5} -4 a^4 z^4+15 a^2 z^4-3 z^4 a^{-2} -12 z^4 a^{-4} +28 z^4-a^5 z^3+8 a^3 z^3+15 a z^3+10 z^3 a^{-1} -4 z^3 a^{-5} +a^4 z^2-7 a^2 z^2+z^2 a^{-2} +5 z^2 a^{-4} -12 z^2-2 a^3 z-4 a z-2 z a^{-1} +z a^{-3} +z a^{-5} +a^2+ a^{-2} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
