K13n3231
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n3231/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -4 t^3+16 t^2-27 t+31-27 t^{-1} +16 t^{-2} -4 t^{-3} }[/math] |
| Conway polynomial | Data:K13n3231/Conway Polynomial |
| Determinant | 125 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -6 z^4 a^{-6} -3 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +3 z^2 a^{-4} -5 z^2 a^{-6} -3 z^2 a^{-8} +4 z^2 a^{-10} + a^{-2} +2 a^{-4} -2 a^{-6} -2 a^{-8} +3 a^{-10} - a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +5 z^{10} a^{-8} +2 z^{10} a^{-10} +5 z^9 a^{-5} +5 z^9 a^{-7} +z^9 a^{-9} +z^9 a^{-11} +5 z^8 a^{-4} +z^8 a^{-6} -10 z^8 a^{-8} -6 z^8 a^{-10} +3 z^7 a^{-3} -8 z^7 a^{-5} -13 z^7 a^{-7} -2 z^7 a^{-9} +z^6 a^{-2} -11 z^6 a^{-4} -18 z^6 a^{-6} +9 z^6 a^{-8} +19 z^6 a^{-10} +4 z^6 a^{-12} -7 z^5 a^{-3} -2 z^5 a^{-5} +4 z^5 a^{-7} +z^5 a^{-9} +3 z^5 a^{-11} +z^5 a^{-13} -3 z^4 a^{-2} +6 z^4 a^{-4} +24 z^4 a^{-6} -3 z^4 a^{-8} -26 z^4 a^{-10} -8 z^4 a^{-12} +3 z^3 a^{-3} +5 z^3 a^{-5} +15 z^3 a^{-7} +7 z^3 a^{-9} -8 z^3 a^{-11} -2 z^3 a^{-13} +3 z^2 a^{-2} -6 z^2 a^{-4} -12 z^2 a^{-6} +8 z^2 a^{-8} +14 z^2 a^{-10} +3 z^2 a^{-12} -4 z a^{-5} -8 z a^{-7} -4 z a^{-9} +z a^{-11} +z a^{-13} - a^{-2} +2 a^{-4} +2 a^{-6} -2 a^{-8} -3 a^{-10} - a^{-12} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
