K12a902
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^5+4 q^4-10 q^3+18 q^2-26 q+32-33 q^{-1} +32 q^{-2} -25 q^{-3} +17 q^{-4} -10 q^{-5} +4 q^{-6} - q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+18 t^2-51 t+71-51 t^{-1} +18 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6+6 z^4+3 z^2+1 }[/math] |
| Determinant | 213 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^2 a^6+2 z^4 a^4-2 a^4-z^6 a^2+z^4 a^2+3 z^2 a^2+3 a^2-z^6+z^4+2 z^2+1+2 z^4 a^{-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}+17 a^2 z^{10}+9 z^{10}+8 a^5 z^9+11 a^3 z^9+16 a z^9+13 z^9 a^{-1} +4 a^6 z^8-20 a^4 z^8-41 a^2 z^8+13 z^8 a^{-2} -4 z^8+a^7 z^7-26 a^5 z^7-56 a^3 z^7-54 a z^7-16 z^7 a^{-1} +9 z^7 a^{-3} -12 a^6 z^6+12 a^4 z^6+29 a^2 z^6-19 z^6 a^{-2} +4 z^6 a^{-4} -18 z^6-3 a^7 z^5+28 a^5 z^5+71 a^3 z^5+54 a z^5+z^5 a^{-1} -12 z^5 a^{-3} +z^5 a^{-5} +9 a^6 z^4-3 a^4 z^4-7 a^2 z^4+12 z^4 a^{-2} -4 z^4 a^{-4} +21 z^4+2 a^7 z^3-16 a^5 z^3-39 a^3 z^3-23 a z^3+6 z^3 a^{-1} +7 z^3 a^{-3} -z^3 a^{-5} -2 a^6 z^2+3 a^4 z^2+3 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} -8 z^2+5 a^5 z+9 a^3 z+4 a z-2 z a^{-1} -2 z a^{-3} -2 a^4-3 a^2+ a^{-2} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
