K12a1156
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+9 q^8-17 q^7+25 q^6-30 q^5+32 q^4-30 q^3+25 q^2-17 q+10-4 q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-8 t^3+25 t^2-43 t+51-43 t^{-1} +25 t^{-2} -8 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8-3 z^4+z^2+1 }[/math] |
| Determinant | 205 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +4 z^6 a^{-4} -2 z^6 a^{-6} -6 z^4 a^{-2} +7 z^4 a^{-4} -6 z^4 a^{-6} +z^4 a^{-8} +z^4-5 z^2 a^{-2} +7 z^2 a^{-4} -5 z^2 a^{-6} +2 z^2 a^{-8} +2 z^2- a^{-2} +2 a^{-4} - a^{-6} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +6 z^{10} a^{-2} +18 z^{10} a^{-4} +12 z^{10} a^{-6} +4 z^9 a^{-1} +7 z^9 a^{-3} +24 z^9 a^{-5} +21 z^9 a^{-7} -19 z^8 a^{-2} -50 z^8 a^{-4} -8 z^8 a^{-6} +22 z^8 a^{-8} +z^8-16 z^7 a^{-1} -58 z^7 a^{-3} -102 z^7 a^{-5} -44 z^7 a^{-7} +16 z^7 a^{-9} +11 z^6 a^{-2} +16 z^6 a^{-4} -51 z^6 a^{-6} -43 z^6 a^{-8} +9 z^6 a^{-10} -4 z^6+22 z^5 a^{-1} +81 z^5 a^{-3} +104 z^5 a^{-5} +21 z^5 a^{-7} -20 z^5 a^{-9} +4 z^5 a^{-11} +12 z^4 a^{-2} +33 z^4 a^{-4} +61 z^4 a^{-6} +28 z^4 a^{-8} -5 z^4 a^{-10} +z^4 a^{-12} +6 z^4-12 z^3 a^{-1} -37 z^3 a^{-3} -35 z^3 a^{-5} -2 z^3 a^{-7} +7 z^3 a^{-9} -z^3 a^{-11} -11 z^2 a^{-2} -19 z^2 a^{-4} -19 z^2 a^{-6} -7 z^2 a^{-8} -4 z^2+2 z a^{-1} +5 z a^{-3} +3 z a^{-5} + a^{-2} +2 a^{-4} + a^{-6} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
