K12a908
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+4 q^9-10 q^8+18 q^7-27 q^6+34 q^5-37 q^4+36 q^3-29 q^2+21 q-12+5 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-22 t^2+55 t-73+55 t^{-1} -22 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+2 z^4+3 z^2+1 }[/math] |
| Determinant | 235 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +2 z^6 a^{-4} +z^6 a^{-6} +3 z^4 a^{-4} +z^4 a^{-6} -z^4 a^{-8} -z^4+2 z^2 a^{-4} +2 z^2 a^{-6} -z^2 a^{-8} + a^{-2} + a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-5} +4 z^{11} a^{-7} +12 z^{10} a^{-4} +21 z^{10} a^{-6} +9 z^{10} a^{-8} +18 z^9 a^{-3} +17 z^9 a^{-5} +7 z^9 a^{-7} +8 z^9 a^{-9} +18 z^8 a^{-2} -9 z^8 a^{-4} -56 z^8 a^{-6} -25 z^8 a^{-8} +4 z^8 a^{-10} +12 z^7 a^{-1} -26 z^7 a^{-3} -58 z^7 a^{-5} -46 z^7 a^{-7} -25 z^7 a^{-9} +z^7 a^{-11} -26 z^6 a^{-2} -12 z^6 a^{-4} +56 z^6 a^{-6} +25 z^6 a^{-8} -12 z^6 a^{-10} +5 z^6+a z^5-13 z^5 a^{-1} +9 z^5 a^{-3} +54 z^5 a^{-5} +60 z^5 a^{-7} +26 z^5 a^{-9} -3 z^5 a^{-11} +10 z^4 a^{-2} +8 z^4 a^{-4} -30 z^4 a^{-6} -16 z^4 a^{-8} +9 z^4 a^{-10} -3 z^4+2 z^3 a^{-1} -z^3 a^{-3} -20 z^3 a^{-5} -33 z^3 a^{-7} -14 z^3 a^{-9} +2 z^3 a^{-11} +2 z^2 a^{-4} +9 z^2 a^{-6} +6 z^2 a^{-8} -z^2 a^{-10} +z a^{-3} +3 z a^{-5} +6 z a^{-7} +4 z a^{-9} - a^{-2} - a^{-6} - a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
