K12a996
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{14}-4 q^{13}+9 q^{12}-16 q^{11}+22 q^{10}-28 q^9+30 q^8-28 q^7+24 q^6-16 q^5+10 q^4-4 q^3+q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ 14 t^2-48 t+69-48 t^{-1} +14 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 14 z^4+8 z^2+1 }[/math] |
| Determinant | 193 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^4 a^{-4} +4 z^4 a^{-6} +6 z^4 a^{-8} +3 z^4 a^{-10} +4 z^2 a^{-6} +8 z^2 a^{-8} -4 z^2 a^{-12} + a^{-6} +3 a^{-8} -2 a^{-10} -2 a^{-12} + a^{-14} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-11} +3 z^{11} a^{-13} +11 z^{10} a^{-10} +17 z^{10} a^{-12} +6 z^{10} a^{-14} +18 z^9 a^{-9} +18 z^9 a^{-11} +4 z^9 a^{-13} +4 z^9 a^{-15} +20 z^8 a^{-8} -12 z^8 a^{-10} -55 z^8 a^{-12} -22 z^8 a^{-14} +z^8 a^{-16} +16 z^7 a^{-7} -33 z^7 a^{-9} -83 z^7 a^{-11} -51 z^7 a^{-13} -17 z^7 a^{-15} +10 z^6 a^{-6} -35 z^6 a^{-8} -26 z^6 a^{-10} +44 z^6 a^{-12} +21 z^6 a^{-14} -4 z^6 a^{-16} +4 z^5 a^{-5} -19 z^5 a^{-7} +7 z^5 a^{-9} +87 z^5 a^{-11} +81 z^5 a^{-13} +24 z^5 a^{-15} +z^4 a^{-4} -8 z^4 a^{-6} +19 z^4 a^{-8} +29 z^4 a^{-10} -5 z^4 a^{-12} -z^4 a^{-14} +5 z^4 a^{-16} +5 z^3 a^{-7} +7 z^3 a^{-9} -28 z^3 a^{-11} -44 z^3 a^{-13} -14 z^3 a^{-15} +4 z^2 a^{-6} -9 z^2 a^{-8} -9 z^2 a^{-10} +3 z^2 a^{-12} -3 z^2 a^{-14} -2 z^2 a^{-16} -5 z a^{-9} +z a^{-11} +9 z a^{-13} +3 z a^{-15} - a^{-6} +3 a^{-8} +2 a^{-10} -2 a^{-12} - a^{-14} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
