K12n269
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+6 q^4-10 q^3+16 q^2-19 q+19-18 q^{-1} +14 q^{-2} -8 q^{-3} +4 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+9 t^2-28 t+41-28 t^{-1} +9 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+3 z^4-z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6+2 a^2 z^4+3 z^4 a^{-2} -2 z^4-a^4 z^2+2 a^2 z^2+5 z^2 a^{-2} -2 z^2 a^{-4} -5 z^2+2 a^2+4 a^{-2} - a^{-4} -4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+4 a z^9+6 z^9 a^{-1} +2 z^9 a^{-3} +7 a^2 z^8+5 z^8 a^{-2} +z^8 a^{-4} +11 z^8+7 a^3 z^7+7 a z^7+z^7 a^{-1} +z^7 a^{-3} +4 a^4 z^6-4 a^2 z^6-z^6 a^{-2} +4 z^6 a^{-4} -13 z^6+a^5 z^5-10 a^3 z^5-22 a z^5-17 z^5 a^{-1} -3 z^5 a^{-3} +3 z^5 a^{-5} -6 a^4 z^4-9 a^2 z^4-20 z^4 a^{-2} -12 z^4 a^{-4} -11 z^4-a^5 z^3+5 a^3 z^3+15 a z^3+13 z^3 a^{-1} -z^3 a^{-3} -5 z^3 a^{-5} +3 a^4 z^2+9 a^2 z^2+20 z^2 a^{-2} +9 z^2 a^{-4} +17 z^2-a^3 z-5 a z-5 z a^{-1} +z a^{-5} -2 a^2-4 a^{-2} - a^{-4} -4 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
