K12n150
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^9+3 q^8-5 q^7+7 q^6-9 q^5+9 q^4-8 q^3+7 q^2-4 q+3- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+10 t^2-9 t+7-9 t^{-1} +10 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+2 z^2+1 }[/math] |
| Determinant | 57 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +6 z^6 a^{-4} -2 z^6 a^{-6} -4 z^4 a^{-2} +13 z^4 a^{-4} -10 z^4 a^{-6} +z^4 a^{-8} -3 z^2 a^{-2} +14 z^2 a^{-4} -14 z^2 a^{-6} +5 z^2 a^{-8} +5 a^{-4} -7 a^{-6} +4 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +3 z^9 a^{-3} +6 z^9 a^{-5} +3 z^9 a^{-7} +3 z^8 a^{-2} +3 z^8 a^{-4} +3 z^8 a^{-6} +3 z^8 a^{-8} +z^7 a^{-1} -12 z^7 a^{-3} -26 z^7 a^{-5} -12 z^7 a^{-7} +z^7 a^{-9} -14 z^6 a^{-2} -30 z^6 a^{-4} -29 z^6 a^{-6} -13 z^6 a^{-8} -4 z^5 a^{-1} +11 z^5 a^{-3} +33 z^5 a^{-5} +17 z^5 a^{-7} -z^5 a^{-9} +18 z^4 a^{-2} +49 z^4 a^{-4} +53 z^4 a^{-6} +25 z^4 a^{-8} +3 z^4 a^{-10} +3 z^3 a^{-1} -4 z^3 a^{-3} -16 z^3 a^{-5} -8 z^3 a^{-7} +2 z^3 a^{-9} +z^3 a^{-11} -8 z^2 a^{-2} -29 z^2 a^{-4} -35 z^2 a^{-6} -18 z^2 a^{-8} -4 z^2 a^{-10} +2 z a^{-3} +3 z a^{-5} +z a^{-7} -z a^{-9} -z a^{-11} +5 a^{-4} +7 a^{-6} +4 a^{-8} + a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
