K12a151
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+3 q^9-6 q^8+11 q^7-16 q^6+20 q^5-23 q^4+22 q^3-18 q^2+14 q-8+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+35 t-47+35 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4+z^2+1 }[/math] |
| Determinant | 147 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +2 z^4 a^{-2} +z^4 a^{-4} -3 z^4 a^{-6} -z^4+3 z^2 a^{-2} +z^2 a^{-4} -5 z^2 a^{-6} +3 z^2 a^{-8} -z^2+2 a^{-2} -3 a^{-6} +3 a^{-8} - a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-5} +z^{11} a^{-7} +4 z^{10} a^{-4} +7 z^{10} a^{-6} +3 z^{10} a^{-8} +7 z^9 a^{-3} +11 z^9 a^{-5} +8 z^9 a^{-7} +4 z^9 a^{-9} +8 z^8 a^{-2} +z^8 a^{-4} -13 z^8 a^{-6} -3 z^8 a^{-8} +3 z^8 a^{-10} +7 z^7 a^{-1} -9 z^7 a^{-3} -39 z^7 a^{-5} -37 z^7 a^{-7} -13 z^7 a^{-9} +z^7 a^{-11} -10 z^6 a^{-2} -16 z^6 a^{-4} -8 z^6 a^{-6} -18 z^6 a^{-8} -12 z^6 a^{-10} +4 z^6+a z^5-10 z^5 a^{-1} +5 z^5 a^{-3} +52 z^5 a^{-5} +50 z^5 a^{-7} +10 z^5 a^{-9} -4 z^5 a^{-11} +21 z^4 a^{-4} +34 z^4 a^{-6} +33 z^4 a^{-8} +14 z^4 a^{-10} -6 z^4-a z^3+2 z^3 a^{-1} -5 z^3 a^{-3} -30 z^3 a^{-5} -29 z^3 a^{-7} -3 z^3 a^{-9} +4 z^3 a^{-11} +3 z^2 a^{-2} -8 z^2 a^{-4} -22 z^2 a^{-6} -20 z^2 a^{-8} -7 z^2 a^{-10} +2 z^2+3 z a^{-3} +8 z a^{-5} +7 z a^{-7} +z a^{-9} -z a^{-11} -2 a^{-2} +3 a^{-6} +3 a^{-8} + a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
