K12n653
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^{10}+3 q^9-4 q^8+6 q^7-6 q^6+6 q^5-5 q^4+4 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+4 t^3-5 t^2+6 t-7+6 t^{-1} -5 t^{-2} +4 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-4 z^6-z^4+6 z^2+1 }[/math] |
| Determinant | 39 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -6 z^6 a^{-6} +z^6 a^{-8} +5 z^4 a^{-4} -11 z^4 a^{-6} +5 z^4 a^{-8} +7 z^2 a^{-4} -7 z^2 a^{-6} +7 z^2 a^{-8} -z^2 a^{-10} +2 a^{-4} -2 a^{-6} +3 a^{-8} -2 a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +4 z^9 a^{-7} +2 z^9 a^{-9} +z^8 a^{-4} -2 z^8 a^{-6} -z^8 a^{-8} +2 z^8 a^{-10} -11 z^7 a^{-5} -19 z^7 a^{-7} -7 z^7 a^{-9} +z^7 a^{-11} -6 z^6 a^{-4} -9 z^6 a^{-6} -11 z^6 a^{-8} -8 z^6 a^{-10} +18 z^5 a^{-5} +25 z^5 a^{-7} +4 z^5 a^{-9} -3 z^5 a^{-11} +12 z^4 a^{-4} +22 z^4 a^{-6} +20 z^4 a^{-8} +11 z^4 a^{-10} +z^4 a^{-12} -9 z^3 a^{-5} -12 z^3 a^{-7} +3 z^3 a^{-11} -9 z^2 a^{-4} -12 z^2 a^{-6} -13 z^2 a^{-8} -10 z^2 a^{-10} +z a^{-5} +3 z a^{-7} -z a^{-9} -z a^{-11} +2 z a^{-13} +2 a^{-4} +2 a^{-6} +3 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. |
