K12n808
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+3 q^7-5 q^6+6 q^5-6 q^4+6 q^3-4 q^2+2 q- q^{-1} + q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^2+8 t-11+8 t^{-1} -2 t^{-2} }[/math] |
| Conway polynomial | [math]\displaystyle{ 1-2 z^4 }[/math] |
| Determinant | 31 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} +z^6 a^{-4} -7 z^4 a^{-2} +5 z^4 a^{-4} -z^4 a^{-6} +z^4-12 z^2 a^{-2} +10 z^2 a^{-4} -2 z^2 a^{-6} +4 z^2-6 a^{-2} +6 a^{-4} -2 a^{-6} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^9 a^{-1} +z^9 a^{-3} +z^8 a^{-2} +2 z^8 a^{-4} +2 z^8 a^{-6} +z^8-8 z^7 a^{-1} -8 z^7 a^{-3} +4 z^7 a^{-5} +4 z^7 a^{-7} -11 z^6 a^{-2} -11 z^6 a^{-4} -4 z^6 a^{-6} +3 z^6 a^{-8} -7 z^6+18 z^5 a^{-1} +20 z^5 a^{-3} -10 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +31 z^4 a^{-2} +27 z^4 a^{-4} +3 z^4 a^{-6} -7 z^4 a^{-8} +14 z^4-13 z^3 a^{-1} -13 z^3 a^{-3} +9 z^3 a^{-5} +7 z^3 a^{-7} -2 z^3 a^{-9} -26 z^2 a^{-2} -22 z^2 a^{-4} -4 z^2 a^{-6} +2 z^2 a^{-8} -10 z^2+2 z a^{-1} +2 z a^{-3} -2 z a^{-5} -2 z a^{-7} +6 a^{-2} +6 a^{-4} +2 a^{-6} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
