K12a843
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-2 q^{11}+4 q^{10}-7 q^9+9 q^8-12 q^7+13 q^6-12 q^5+10 q^4-7 q^3+5 q^2-2 q+1 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+11 t^2-18 t+21-18 t^{-1} +11 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-7 z^4-z^2+1 }[/math] |
| Determinant | 85 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-4} -z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -3 z^4 a^{-4} -2 z^4 a^{-6} -4 z^4 a^{-8} +z^4 a^{-10} +3 z^2 a^{-2} -2 z^2 a^{-4} +z^2 a^{-6} -6 z^2 a^{-8} +3 z^2 a^{-10} +2 a^{-2} - a^{-4} +2 a^{-6} -4 a^{-8} +2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +2 z^{10} a^{-6} +5 z^{10} a^{-8} +3 z^{10} a^{-10} +2 z^9 a^{-5} -z^9 a^{-7} +z^9 a^{-9} +4 z^9 a^{-11} +2 z^8 a^{-4} -7 z^8 a^{-6} -25 z^8 a^{-8} -13 z^8 a^{-10} +3 z^8 a^{-12} +2 z^7 a^{-3} -4 z^7 a^{-5} -7 z^7 a^{-7} -22 z^7 a^{-9} -19 z^7 a^{-11} +2 z^7 a^{-13} +z^6 a^{-2} -3 z^6 a^{-4} +14 z^6 a^{-6} +50 z^6 a^{-8} +20 z^6 a^{-10} -11 z^6 a^{-12} +z^6 a^{-14} -6 z^5 a^{-3} +2 z^5 a^{-5} +23 z^5 a^{-7} +56 z^5 a^{-9} +34 z^5 a^{-11} -7 z^5 a^{-13} -4 z^4 a^{-2} -5 z^4 a^{-4} -17 z^4 a^{-6} -41 z^4 a^{-8} -11 z^4 a^{-10} +10 z^4 a^{-12} -4 z^4 a^{-14} +3 z^3 a^{-3} -4 z^3 a^{-5} -20 z^3 a^{-7} -46 z^3 a^{-9} -29 z^3 a^{-11} +4 z^3 a^{-13} +5 z^2 a^{-2} +5 z^2 a^{-4} +9 z^2 a^{-6} +20 z^2 a^{-8} +4 z^2 a^{-10} -4 z^2 a^{-12} +3 z^2 a^{-14} +z a^{-3} +z a^{-5} +6 z a^{-7} +14 z a^{-9} +8 z a^{-11} -2 a^{-2} - a^{-4} -2 a^{-6} -4 a^{-8} -2 a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
