K13n411
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n411/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-18 t^2+32 t-37+32 t^{-1} -18 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | Data:K13n411/Conway Polynomial |
| Determinant | 151 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +2 z^6 a^{-4} +z^6-10 z^4 a^{-2} +7 z^4 a^{-4} -z^4 a^{-6} +2 z^4+a^2 z^2-8 z^2 a^{-2} +8 z^2 a^{-4} -2 z^2 a^{-6} -z^2+2 a^2- a^{-2} +3 a^{-4} - a^{-6} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-1} +z^{11} a^{-3} +6 z^{10} a^{-2} +4 z^{10} a^{-4} +2 z^{10}+a z^9+3 z^9 a^{-1} +10 z^9 a^{-3} +8 z^9 a^{-5} -9 z^8 a^{-2} +5 z^8 a^{-4} +10 z^8 a^{-6} -4 z^8+a z^7-8 z^7 a^{-1} -25 z^7 a^{-3} -8 z^7 a^{-5} +8 z^7 a^{-7} +3 a^2 z^6+z^6 a^{-2} -24 z^6 a^{-4} -16 z^6 a^{-6} +4 z^6 a^{-8} +8 z^6-9 a z^5+2 z^5 a^{-1} +22 z^5 a^{-3} -2 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} -10 a^2 z^4+4 z^4 a^{-2} +28 z^4 a^{-4} +10 z^4 a^{-6} -5 z^4 a^{-8} -19 z^4+8 a z^3+z^3 a^{-1} -8 z^3 a^{-3} +5 z^3 a^{-5} +5 z^3 a^{-7} -z^3 a^{-9} +9 a^2 z^2-4 z^2 a^{-2} -14 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} +14 z^2-2 a z-z a^{-1} +z a^{-3} -z a^{-5} -z a^{-7} -2 a^2+ a^{-2} +3 a^{-4} + a^{-6} -2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
