K12n565
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^2-2 q+3-5 q^{-1} +7 q^{-2} -6 q^{-3} +7 q^{-4} -6 q^{-5} +4 q^{-6} -3 q^{-7} + q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^3+7 t^2-9 t+9-9 t^{-1} +7 t^{-2} -2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^6-5 z^4+z^2+1 }[/math] |
| Determinant | 45 |
| Signature | -4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^6+2 z^2 a^6-a^6-z^6 a^4-3 z^4 a^4+2 a^4-z^6 a^2-4 z^4 a^2-4 z^2 a^2-a^2+z^4+3 z^2+1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^2 a^{10}+3 z^3 a^9-z a^9+z^6 a^8+z^2 a^8+2 z^7 a^7-4 z^5 a^7+4 z^3 a^7-3 z a^7+2 z^8 a^6-3 z^6 a^6-4 z^4 a^6+3 z^2 a^6+a^6+2 z^9 a^5-6 z^7 a^5+5 z^5 a^5-5 z^3 a^5+z^{10} a^4-2 z^8 a^4-z^6 a^4-3 z^4 a^4+3 z^2 a^4+2 a^4+4 z^9 a^3-20 z^7 a^3+32 z^5 a^3-21 z^3 a^3+4 z a^3+z^{10} a^2-3 z^8 a^2-3 z^6 a^2+12 z^4 a^2-6 z^2 a^2+a^2+2 z^9 a-12 z^7 a+23 z^5 a-15 z^3 a+2 z a+z^8-6 z^6+11 z^4-6 z^2+1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
