K12a919
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+16 q^2-23 q+28-29 q^{-1} +28 q^{-2} -22 q^{-3} +15 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+16 t^2-45 t+63-45 t^{-1} +16 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+4 z^4+z^2+1 }[/math] |
| Determinant | 189 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6+2 z^4 a^4+z^2 a^4-a^4-z^6 a^2+z^2 a^2+2 a^2-z^6+2 z^4 a^{-2} +z^2 a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^3 z^{11}+3 a z^{11}+8 a^4 z^{10}+16 a^2 z^{10}+8 z^{10}+8 a^5 z^9+7 a^3 z^9+9 a z^9+10 z^9 a^{-1} +4 a^6 z^8-25 a^4 z^8-51 a^2 z^8+10 z^8 a^{-2} -12 z^8+a^7 z^7-29 a^5 z^7-52 a^3 z^7-42 a z^7-12 z^7 a^{-1} +8 z^7 a^{-3} -13 a^6 z^6+21 a^4 z^6+61 a^2 z^6-11 z^6 a^{-2} +4 z^6 a^{-4} +12 z^6-3 a^7 z^5+31 a^5 z^5+75 a^3 z^5+57 a z^5+4 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4-6 a^4 z^4-33 a^2 z^4-5 z^4 a^{-4} -13 z^4+a^7 z^3-14 a^5 z^3-38 a^3 z^3-33 a z^3-4 z^3 a^{-1} +5 z^3 a^{-3} -z^3 a^{-5} -2 a^6 z^2+3 a^4 z^2+9 a^2 z^2+2 z^2 a^{-2} +2 z^2 a^{-4} +4 z^2+3 a^5 z+7 a^3 z+6 a z+2 z a^{-1} -a^4-2 a^2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
