K12a842
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+3 q^5-6 q^4+9 q^3-11 q^2+13 q-13+12 q^{-1} -9 q^{-2} +7 q^{-3} -4 q^{-4} +2 q^{-5} - q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 3 t^3-11 t^2+20 t-23+20 t^{-1} -11 t^{-2} +3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 3 z^6+7 z^4+3 z^2+1 }[/math] |
| Determinant | 91 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ a^2 z^6+z^6 a^{-2} +z^6-a^4 z^4+4 a^2 z^4+3 z^4 a^{-2} -z^4 a^{-4} +2 z^4-3 a^4 z^2+6 a^2 z^2+3 z^2 a^{-2} -2 z^2 a^{-4} -z^2-2 a^4+4 a^2+2 a^{-2} - a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+2 a^4 z^{10}+6 a^2 z^{10}+4 z^{10}+a^5 z^9-a^3 z^9+5 a z^9+7 z^9 a^{-1} -13 a^4 z^8-32 a^2 z^8+9 z^8 a^{-2} -10 z^8-7 a^5 z^7-19 a^3 z^7-41 a z^7-19 z^7 a^{-1} +10 z^7 a^{-3} +29 a^4 z^6+55 a^2 z^6-20 z^6 a^{-2} +9 z^6 a^{-4} -3 z^6+17 a^5 z^5+55 a^3 z^5+71 a z^5+8 z^5 a^{-1} -19 z^5 a^{-3} +6 z^5 a^{-5} -27 a^4 z^4-38 a^2 z^4+4 z^4 a^{-2} -13 z^4 a^{-4} +3 z^4 a^{-6} +9 z^4-17 a^5 z^3-49 a^3 z^3-43 a z^3+6 z^3 a^{-3} -4 z^3 a^{-5} +z^3 a^{-7} +11 a^4 z^2+15 a^2 z^2+4 z^2 a^{-2} +5 z^2 a^{-4} +3 z^2+6 a^5 z+13 a^3 z+9 a z+z a^{-1} +z a^{-5} -2 a^4-4 a^2-2 a^{-2} - a^{-4} -2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
