K12n496
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{12}-4 q^{11}+8 q^{10}-14 q^9+17 q^8-19 q^7+20 q^6-15 q^5+11 q^4-6 q^3+2 q^2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^3+11 t^2-28 t+37-28 t^{-1} +11 t^{-2} - t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^6+5 z^4+7 z^2+1 }[/math] |
| Determinant | 117 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-6} +2 z^4 a^{-4} -z^4 a^{-6} +4 z^4 a^{-8} +3 z^2 a^{-4} +z^2 a^{-6} +7 z^2 a^{-8} -4 z^2 a^{-10} +2 a^{-6} +2 a^{-8} -4 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-8} +z^{10} a^{-10} +3 z^9 a^{-7} +7 z^9 a^{-9} +4 z^9 a^{-11} +3 z^8 a^{-6} +10 z^8 a^{-8} +13 z^8 a^{-10} +6 z^8 a^{-12} +z^7 a^{-5} +2 z^7 a^{-7} +3 z^7 a^{-11} +4 z^7 a^{-13} +z^6 a^{-6} -18 z^6 a^{-8} -32 z^6 a^{-10} -12 z^6 a^{-12} +z^6 a^{-14} +5 z^5 a^{-5} -4 z^5 a^{-7} -27 z^5 a^{-9} -28 z^5 a^{-11} -10 z^5 a^{-13} +3 z^4 a^{-4} -4 z^4 a^{-6} +7 z^4 a^{-8} +20 z^4 a^{-10} +4 z^4 a^{-12} -2 z^4 a^{-14} -6 z^3 a^{-5} +2 z^3 a^{-7} +29 z^3 a^{-9} +29 z^3 a^{-11} +8 z^3 a^{-13} -3 z^2 a^{-4} +6 z^2 a^{-6} +2 z^2 a^{-8} -8 z^2 a^{-10} +z^2 a^{-14} -z a^{-7} -11 z a^{-9} -12 z a^{-11} -2 z a^{-13} -2 a^{-6} +2 a^{-8} +4 a^{-10} + a^{-12} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
