K13n1812
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n1812/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+15 t^2-21 t+23-21 t^{-1} +15 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13n1812/Conway Polynomial |
| Determinant | 109 |
| 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} +9 z^4 a^{-4} -3 z^4 a^{-6} +z^4-9 z^2 a^{-2} +8 z^2 a^{-4} -z^2 a^{-6} +3 z^2-3 a^{-2} +2 a^{-4} + a^{-6} - a^{-8} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +3 z^9 a^{-1} +6 z^9 a^{-3} +6 z^9 a^{-5} +3 z^9 a^{-7} -8 z^8 a^{-2} -13 z^8 a^{-4} -3 z^8 a^{-6} +z^8 a^{-8} +z^8-14 z^7 a^{-1} -36 z^7 a^{-3} -24 z^7 a^{-5} -2 z^7 a^{-7} -7 z^6 a^{-2} -14 z^6 a^{-4} -5 z^6 a^{-6} +7 z^6 a^{-8} -5 z^6+21 z^5 a^{-1} +43 z^5 a^{-3} +12 z^5 a^{-5} -3 z^5 a^{-7} +7 z^5 a^{-9} +29 z^4 a^{-2} +33 z^4 a^{-4} -3 z^4 a^{-6} -13 z^4 a^{-8} +3 z^4 a^{-10} +9 z^4-11 z^3 a^{-1} -12 z^3 a^{-3} +4 z^3 a^{-5} -2 z^3 a^{-7} -6 z^3 a^{-9} +z^3 a^{-11} -19 z^2 a^{-2} -14 z^2 a^{-4} +5 z^2 a^{-6} +7 z^2 a^{-8} -7 z^2+z a^{-1} -2 z a^{-5} +z a^{-7} +2 z a^{-9} +3 a^{-2} +2 a^{-4} - a^{-6} - a^{-8} +2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
