K12n697
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+2 q^9-2 q^8+q^7+q^6-3 q^5+4 q^4-5 q^3+6 q^2-4 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+6 t^2-t-3- t^{-1} +6 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 21 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +6 z^6 a^{-4} -z^6 a^{-6} -4 z^4 a^{-2} +12 z^4 a^{-4} -6 z^4 a^{-6} -3 z^2 a^{-2} +12 z^2 a^{-4} -9 z^2 a^{-6} +3 z^2 a^{-8} +4 a^{-4} -5 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +3 z^9 a^{-3} +4 z^9 a^{-5} +2 z^9 a^{-7} +z^9 a^{-9} +3 z^8 a^{-2} -3 z^8 a^{-6} +2 z^8 a^{-8} +2 z^8 a^{-10} +z^7 a^{-1} -13 z^7 a^{-3} -22 z^7 a^{-5} -14 z^7 a^{-7} -5 z^7 a^{-9} +z^7 a^{-11} -14 z^6 a^{-2} -20 z^6 a^{-4} -11 z^6 a^{-6} -16 z^6 a^{-8} -11 z^6 a^{-10} -4 z^5 a^{-1} +12 z^5 a^{-3} +32 z^5 a^{-5} +23 z^5 a^{-7} +2 z^5 a^{-9} -5 z^5 a^{-11} +17 z^4 a^{-2} +36 z^4 a^{-4} +32 z^4 a^{-6} +28 z^4 a^{-8} +15 z^4 a^{-10} +3 z^3 a^{-1} -4 z^3 a^{-3} -18 z^3 a^{-5} -13 z^3 a^{-7} +4 z^3 a^{-9} +6 z^3 a^{-11} -7 z^2 a^{-2} -22 z^2 a^{-4} -24 z^2 a^{-6} -16 z^2 a^{-8} -7 z^2 a^{-10} +2 z a^{-3} +4 z a^{-5} +3 z a^{-7} -z a^{-9} -2 z a^{-11} +4 a^{-4} +5 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
