K12n533
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^6+5 q^5-7 q^4+10 q^3-11 q^2+10 q-8+6 q^{-1} -3 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-8 t^2+12 t-13+12 t^{-1} -8 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-4 z^4+1 }[/math] |
| Determinant | 63 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +z^6-13 z^4 a^{-2} +5 z^4 a^{-4} +4 z^4-13 z^2 a^{-2} +9 z^2 a^{-4} -z^2 a^{-6} +5 z^2-6 a^{-2} +6 a^{-4} -2 a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +4 z^9 a^{-1} +5 z^9 a^{-3} +z^9 a^{-5} +4 z^8 a^{-2} -z^8 a^{-4} +5 z^8+3 a z^7-13 z^7 a^{-1} -19 z^7 a^{-3} -3 z^7 a^{-5} +a^2 z^6-28 z^6 a^{-2} -8 z^6 a^{-4} +z^6 a^{-6} -18 z^6-9 a z^5+10 z^5 a^{-1} +24 z^5 a^{-3} +5 z^5 a^{-5} -3 a^2 z^4+46 z^4 a^{-2} +28 z^4 a^{-4} +3 z^4 a^{-6} +18 z^4+4 a z^3-z^3 a^{-1} -5 z^3 a^{-3} +2 z^3 a^{-5} +2 z^3 a^{-7} +a^2 z^2-28 z^2 a^{-2} -24 z^2 a^{-4} -7 z^2 a^{-6} -10 z^2-a z-z a^{-1} -z a^{-3} -3 z a^{-5} -2 z a^{-7} +6 a^{-2} +6 a^{-4} +2 a^{-6} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
