K12n675
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^7+2 q^6-4 q^5+5 q^4-6 q^3+8 q^2-6 q+6-4 q^{-1} +2 q^{-2} - q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-3 t^3+6 t^2-8 t+9-8 t^{-1} +6 t^{-2} -3 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+5 z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 45 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +7 z^6 a^{-2} -z^6 a^{-4} -z^6+18 z^4 a^{-2} -5 z^4 a^{-4} -5 z^4+21 z^2 a^{-2} -8 z^2 a^{-4} -8 z^2+10 a^{-2} -5 a^{-4} -4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^9 a^{-1} +3 z^9 a^{-3} +2 z^9 a^{-5} -5 z^8 a^{-2} -3 z^8 a^{-4} +2 z^8 a^{-6} -4 z^7 a^{-1} -13 z^7 a^{-3} -8 z^7 a^{-5} +z^7 a^{-7} +16 z^6 a^{-2} +3 z^6 a^{-4} -9 z^6 a^{-6} +4 z^6+3 a z^5+13 z^5 a^{-1} +22 z^5 a^{-3} +7 z^5 a^{-5} -5 z^5 a^{-7} +2 a^2 z^4-29 z^4 a^{-2} -9 z^4 a^{-4} +10 z^4 a^{-6} -8 z^4+a^3 z^3-3 a z^3-19 z^3 a^{-1} -23 z^3 a^{-3} -z^3 a^{-5} +7 z^3 a^{-7} -a^2 z^2+24 z^2 a^{-2} +12 z^2 a^{-4} -2 z^2 a^{-6} +9 z^2-a^3 z+2 a z+9 z a^{-1} +10 z a^{-3} +z a^{-5} -3 z a^{-7} -10 a^{-2} -5 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. |
