K12n524
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^7-5 q^6+9 q^5-13 q^4+15 q^3-15 q^2+13 q-10+6 q^{-1} -2 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-11 t^2+21 t-23+21 t^{-1} -11 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+z^4-5 z^2+1 }[/math] |
| Determinant | 91 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6 a^{-4} +z^4 a^{-2} +3 z^4 a^{-4} -z^4 a^{-6} -2 z^4+a^2 z^2-3 z^2 a^{-2} +4 z^2 a^{-4} -3 z^2 a^{-6} -4 z^2+2 a^2-2 a^{-2} +3 a^{-4} -2 a^{-6} + a^{-8} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +3 z^9 a^{-1} +6 z^9 a^{-3} +3 z^9 a^{-5} +5 z^8 a^{-2} +5 z^8 a^{-4} +3 z^8 a^{-6} +3 z^8+2 a z^7-6 z^7 a^{-1} -14 z^7 a^{-3} -5 z^7 a^{-5} +z^7 a^{-7} +a^2 z^6-17 z^6 a^{-2} -15 z^6 a^{-4} -5 z^6 a^{-6} -6 z^6-5 a z^5+8 z^5 a^{-1} +19 z^5 a^{-3} +9 z^5 a^{-5} +3 z^5 a^{-7} -4 a^2 z^4+20 z^4 a^{-2} +21 z^4 a^{-4} +9 z^4 a^{-6} +3 z^4 a^{-8} +z^4+2 a z^3-13 z^3 a^{-1} -15 z^3 a^{-3} -6 z^3 a^{-5} -6 z^3 a^{-7} +5 a^2 z^2-13 z^2 a^{-2} -12 z^2 a^{-4} -7 z^2 a^{-6} -5 z^2 a^{-8} +2 z^2+a z+5 z a^{-1} +4 z a^{-3} +2 z a^{-5} +2 z a^{-7} -2 a^2+2 a^{-2} +3 a^{-4} +2 a^{-6} + a^{-8} -1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
