K12n817
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-2 q^5+4 q^4-6 q^3+7 q^2-8 q+8-6 q^{-1} +4 q^{-2} -2 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+6 t^2-10 t+13-10 t^{-1} +6 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-6 z^4-4 z^2+1 }[/math] |
| Determinant | 49 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} -z^6+a^2 z^4-4 z^4 a^{-2} +z^4 a^{-4} -4 z^4+3 a^2 z^2-5 z^2 a^{-2} +3 z^2 a^{-4} -5 z^2+2 a^2-2 a^{-2} +2 a^{-4} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+a z^9+4 z^9 a^{-1} +3 z^9 a^{-3} -z^8 a^{-2} +3 z^8 a^{-4} -4 z^8-4 a z^7-20 z^7 a^{-1} -14 z^7 a^{-3} +2 z^7 a^{-5} +3 a^2 z^6-9 z^6 a^{-2} -12 z^6 a^{-4} +z^6 a^{-6} +7 z^6+2 a^3 z^5+9 a z^5+38 z^5 a^{-1} +24 z^5 a^{-3} -7 z^5 a^{-5} +a^4 z^4-7 a^2 z^4+22 z^4 a^{-2} +14 z^4 a^{-4} -4 z^4 a^{-6} -4 z^4-4 a^3 z^3-7 a z^3-27 z^3 a^{-1} -20 z^3 a^{-3} +4 z^3 a^{-5} -2 a^4 z^2+6 a^2 z^2-15 z^2 a^{-2} -9 z^2 a^{-4} +3 z^2 a^{-6} +5 z^2+a^3 z+3 a z+7 z a^{-1} +5 z a^{-3} -2 a^2+2 a^{-2} +2 a^{-4} -1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
