K12n49
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^6-3 q^5+7 q^4-10 q^3+12 q^2-14 q+13-10 q^{-1} +7 q^{-2} -3 q^{-3} + q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^2-20 t+33-20 t^{-1} +4 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^4-4 z^2+1 }[/math] |
| Determinant | 81 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^4-3 z^2 a^2-a^2+2 z^4+z^2+1+2 z^4 a^{-2} +z^2 a^{-2} -3 z^2 a^{-4} - a^{-4} + a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+2 a z^9+5 z^9 a^{-1} +3 z^9 a^{-3} +a^2 z^8+4 z^8 a^{-2} +4 z^8 a^{-4} +z^8-6 a z^7-12 z^7 a^{-1} -3 z^7 a^{-3} +3 z^7 a^{-5} -a^2 z^6-13 z^6 a^{-2} -8 z^6 a^{-4} +z^6 a^{-6} -5 z^6+3 a^3 z^5+15 a z^5+14 z^5 a^{-1} -6 z^5 a^{-3} -8 z^5 a^{-5} +a^4 z^4+6 a^2 z^4+9 z^4 a^{-2} -z^4 a^{-4} -3 z^4 a^{-6} +12 z^4-4 a^3 z^3-10 a z^3-9 z^3 a^{-1} +2 z^3 a^{-3} +5 z^3 a^{-5} -2 a^4 z^2-6 a^2 z^2-3 z^2 a^{-2} +3 z^2 a^{-4} +3 z^2 a^{-6} -7 z^2+a^3 z+2 a z+4 z a^{-1} +2 z a^{-3} -z a^{-5} +a^4+a^2- a^{-4} - a^{-6} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
