K12a553
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{11}+4 q^{10}-10 q^9+17 q^8-25 q^7+31 q^6-32 q^5+30 q^4-24 q^3+17 q^2-9 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-10 t^3+26 t^2-41 t+47-41 t^{-1} +26 t^{-2} -10 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^8+6 z^6+6 z^4+5 z^2+1 }[/math] |
| Determinant | 205 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +4 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-2} +6 z^4 a^{-4} +6 z^4 a^{-6} -3 z^4 a^{-8} -2 z^2 a^{-2} +5 z^2 a^{-4} +5 z^2 a^{-6} -3 z^2 a^{-8} + a^{-4} +2 a^{-6} -2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +5 z^{10} a^{-4} +13 z^{10} a^{-6} +8 z^{10} a^{-8} +6 z^9 a^{-3} +12 z^9 a^{-5} +19 z^9 a^{-7} +13 z^9 a^{-9} +4 z^8 a^{-2} -2 z^8 a^{-4} -21 z^8 a^{-6} -2 z^8 a^{-8} +13 z^8 a^{-10} +z^7 a^{-1} -14 z^7 a^{-3} -40 z^7 a^{-5} -55 z^7 a^{-7} -21 z^7 a^{-9} +9 z^7 a^{-11} -13 z^6 a^{-2} -24 z^6 a^{-4} -2 z^6 a^{-6} -17 z^6 a^{-8} -22 z^6 a^{-10} +4 z^6 a^{-12} -3 z^5 a^{-1} +4 z^5 a^{-3} +30 z^5 a^{-5} +52 z^5 a^{-7} +15 z^5 a^{-9} -13 z^5 a^{-11} +z^5 a^{-13} +14 z^4 a^{-2} +28 z^4 a^{-4} +8 z^4 a^{-6} +15 z^4 a^{-8} +17 z^4 a^{-10} -4 z^4 a^{-12} +3 z^3 a^{-1} +6 z^3 a^{-3} -8 z^3 a^{-5} -24 z^3 a^{-7} -5 z^3 a^{-9} +7 z^3 a^{-11} -z^3 a^{-13} -5 z^2 a^{-2} -10 z^2 a^{-4} +z^2 a^{-6} +z^2 a^{-8} -5 z^2 a^{-10} -z a^{-1} -2 z a^{-3} +5 z a^{-7} +2 z a^{-9} -2 z a^{-11} + a^{-4} -2 a^{-6} -2 a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
