K12n455
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{10}-4 q^9+8 q^8-12 q^7+15 q^6-16 q^5+15 q^4-12 q^3+8 q^2-4 q+2 }[/math] |
| Alexander polynomial | [math]\displaystyle{ -3 t^3+12 t^2-21 t+25-21 t^{-1} +12 t^{-2} -3 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ -3 z^6-6 z^4+1 }[/math] |
| Determinant | 97 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 z^6 a^{-4} -z^6 a^{-6} +2 z^4 a^{-2} -8 z^4 a^{-4} -z^4 a^{-6} +z^4 a^{-8} +6 z^2 a^{-2} -11 z^2 a^{-4} +4 z^2 a^{-6} +z^2 a^{-8} +4 a^{-2} -6 a^{-4} +4 a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-3} +5 z^9 a^{-5} +4 z^9 a^{-7} -z^8 a^{-4} +7 z^8 a^{-6} +8 z^8 a^{-8} -z^7 a^{-3} -9 z^7 a^{-5} +2 z^7 a^{-7} +10 z^7 a^{-9} +3 z^6 a^{-2} +5 z^6 a^{-4} -14 z^6 a^{-6} -8 z^6 a^{-8} +8 z^6 a^{-10} -3 z^5 a^{-3} +z^5 a^{-5} -13 z^5 a^{-7} -13 z^5 a^{-9} +4 z^5 a^{-11} -11 z^4 a^{-2} -22 z^4 a^{-4} -4 z^4 a^{-6} -2 z^4 a^{-8} -8 z^4 a^{-10} +z^4 a^{-12} +3 z^3 a^{-3} +z^3 a^{-5} +5 z^3 a^{-7} +5 z^3 a^{-9} -2 z^3 a^{-11} +12 z^2 a^{-2} +23 z^2 a^{-4} +12 z^2 a^{-6} +3 z^2 a^{-8} +2 z^2 a^{-10} -4 a^{-2} -6 a^{-4} -4 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. |
