K12n871
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-9 q^8+14 q^7-18 q^6+20 q^5-19 q^4+16 q^3-11 q^2+6 q-1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^3-9 t^2+29 t-41+29 t^{-1} -9 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^6-3 z^4+2 z^2+1 }[/math] |
| Determinant | 119 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-4} -z^4 a^{-2} +2 z^4 a^{-4} -4 z^4 a^{-6} +z^2 a^{-2} +4 z^2 a^{-4} -7 z^2 a^{-6} +4 z^2 a^{-8} + a^{-2} +2 a^{-4} -4 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-6} +3 z^{10} a^{-8} +9 z^9 a^{-5} +15 z^9 a^{-7} +6 z^9 a^{-9} +9 z^8 a^{-4} +9 z^8 a^{-6} +4 z^8 a^{-8} +4 z^8 a^{-10} +3 z^7 a^{-3} -23 z^7 a^{-5} -44 z^7 a^{-7} -17 z^7 a^{-9} +z^7 a^{-11} -23 z^6 a^{-4} -48 z^6 a^{-6} -38 z^6 a^{-8} -13 z^6 a^{-10} +2 z^5 a^{-3} +24 z^5 a^{-5} +34 z^5 a^{-7} +9 z^5 a^{-9} -3 z^5 a^{-11} +6 z^4 a^{-2} +30 z^4 a^{-4} +54 z^4 a^{-6} +43 z^4 a^{-8} +13 z^4 a^{-10} +z^3 a^{-1} -z^3 a^{-3} -13 z^3 a^{-5} -12 z^3 a^{-7} +2 z^3 a^{-9} +3 z^3 a^{-11} -z^2 a^{-2} -14 z^2 a^{-4} -26 z^2 a^{-6} -18 z^2 a^{-8} -5 z^2 a^{-10} +z a^{-3} +2 z a^{-5} +2 z a^{-7} -z a^{-11} - a^{-2} +2 a^{-4} +4 a^{-6} +3 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. |
