K13n1867
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n1867/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+13 t^2-11 t+7-11 t^{-1} +13 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13n1867/Conway Polynomial |
| Determinant | 69 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -8 z^4 a^{-2} +8 z^4 a^{-4} -4 z^4 a^{-6} +z^4-7 z^2 a^{-2} +8 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} +3 z^2-2 a^{-2} +3 a^{-4} - a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +5 z^{10} a^{-4} +2 z^{10} a^{-6} +3 z^9 a^{-1} +3 z^9 a^{-3} +z^9 a^{-5} +z^9 a^{-7} -11 z^8 a^{-2} -18 z^8 a^{-4} -6 z^8 a^{-6} +z^8-15 z^7 a^{-1} -30 z^7 a^{-3} -18 z^7 a^{-5} -3 z^7 a^{-7} +3 z^6 a^{-2} +6 z^6 a^{-4} -2 z^6 a^{-6} -5 z^6+23 z^5 a^{-1} +45 z^5 a^{-3} +24 z^5 a^{-5} +2 z^5 a^{-7} +15 z^4 a^{-2} +18 z^4 a^{-4} +12 z^4 a^{-6} +z^4 a^{-8} +8 z^4-13 z^3 a^{-1} -22 z^3 a^{-3} -11 z^3 a^{-5} -3 z^3 a^{-7} -z^3 a^{-9} -11 z^2 a^{-2} -14 z^2 a^{-4} -8 z^2 a^{-6} -5 z^2+2 z a^{-1} +4 z a^{-3} +2 z a^{-5} +3 z a^{-7} +3 z a^{-9} +2 a^{-2} +3 a^{-4} - a^{-8} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
