K12a769
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-9 q^3+17 q^2-24 q+28-30 q^{-1} +28 q^{-2} -21 q^{-3} +15 q^{-4} -8 q^{-5} +3 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-a^6+2 z^4 a^4+2 z^2 a^4+a^4-z^6 a^2+z^2 a^2+2 a^2-z^6-z^2-2+2 z^4 a^{-2} +z^2 a^{-2} + a^{-2} -z^2 a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^3 z^{11}+2 a z^{11}+5 a^4 z^{10}+12 a^2 z^{10}+7 z^{10}+5 a^5 z^9+8 a^3 z^9+14 a z^9+11 z^9 a^{-1} +3 a^6 z^8-10 a^4 z^8-27 a^2 z^8+11 z^8 a^{-2} -3 z^8+a^7 z^7-14 a^5 z^7-34 a^3 z^7-42 a z^7-15 z^7 a^{-1} +8 z^7 a^{-3} -10 a^6 z^6+3 a^4 z^6+25 a^2 z^6-14 z^6 a^{-2} +4 z^6 a^{-4} -6 z^6-4 a^7 z^5+10 a^5 z^5+38 a^3 z^5+44 a z^5+9 z^5 a^{-1} -10 z^5 a^{-3} +z^5 a^{-5} +10 a^6 z^4-2 a^4 z^4-23 a^2 z^4+4 z^4 a^{-2} -5 z^4 a^{-4} -2 z^4+5 a^7 z^3-a^5 z^3-20 a^3 z^3-23 a z^3-4 z^3 a^{-1} +4 z^3 a^{-3} -z^3 a^{-5} -4 a^6 z^2+3 a^4 z^2+14 a^2 z^2+3 z^2 a^{-2} +2 z^2 a^{-4} +8 z^2-2 a^7 z-a^5 z+3 a^3 z+2 a z+a^6+a^4-2 a^2- a^{-2} -2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
