K13a3966
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a3966/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -6 t^3+35 t^2-80 t+103-80 t^{-1} +35 t^{-2} -6 t^{-3} }[/math] |
| Conway polynomial | Data:K13a3966/Conway Polynomial |
| Determinant | 345 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -3 z^6 a^{-6} -2 z^6 a^{-8} +z^4 a^{-2} +z^4 a^{-4} -4 z^4 a^{-6} -2 z^4 a^{-8} +3 z^4 a^{-10} +z^2 a^{-2} +3 z^2 a^{-4} +z^2 a^{-6} -2 z^2 a^{-8} +4 z^2 a^{-10} -z^2 a^{-12} + a^{-4} +2 a^{-6} -3 a^{-8} +2 a^{-10} - a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{12} a^{-8} +3 z^{12} a^{-10} +10 z^{11} a^{-7} +19 z^{11} a^{-9} +9 z^{11} a^{-11} +15 z^{10} a^{-6} +23 z^{10} a^{-8} +20 z^{10} a^{-10} +12 z^{10} a^{-12} +14 z^9 a^{-5} -3 z^9 a^{-7} -34 z^9 a^{-9} -8 z^9 a^{-11} +9 z^9 a^{-13} +9 z^8 a^{-4} -25 z^8 a^{-6} -70 z^8 a^{-8} -71 z^8 a^{-10} -31 z^8 a^{-12} +4 z^8 a^{-14} +4 z^7 a^{-3} -26 z^7 a^{-5} -21 z^7 a^{-7} +12 z^7 a^{-9} -24 z^7 a^{-11} -26 z^7 a^{-13} +z^7 a^{-15} +z^6 a^{-2} -16 z^6 a^{-4} +18 z^6 a^{-6} +80 z^6 a^{-8} +85 z^6 a^{-10} +29 z^6 a^{-12} -11 z^6 a^{-14} -7 z^5 a^{-3} +21 z^5 a^{-5} +25 z^5 a^{-7} +9 z^5 a^{-9} +42 z^5 a^{-11} +27 z^5 a^{-13} -3 z^5 a^{-15} -2 z^4 a^{-2} +11 z^4 a^{-4} -7 z^4 a^{-6} -47 z^4 a^{-8} -51 z^4 a^{-10} -16 z^4 a^{-12} +8 z^4 a^{-14} +3 z^3 a^{-3} -8 z^3 a^{-5} -10 z^3 a^{-7} -6 z^3 a^{-9} -25 z^3 a^{-11} -16 z^3 a^{-13} +2 z^3 a^{-15} +z^2 a^{-2} -5 z^2 a^{-4} +2 z^2 a^{-6} +16 z^2 a^{-8} +15 z^2 a^{-10} +5 z^2 a^{-12} -2 z^2 a^{-14} +2 z a^{-7} +2 z a^{-9} +4 z a^{-11} +4 z a^{-13} + a^{-4} -2 a^{-6} -3 a^{-8} -2 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. |
