K12n2
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+4 q^5-8 q^4+11 q^3-13 q^2+14 q-12+10 q^{-1} -6 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-11 t^2+16 t-17+16 t^{-1} -11 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6-z^4+z^2+1 }[/math] |
| Determinant | 83 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -6 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-14 z^4 a^{-2} +5 z^4 a^{-4} +9 z^4-3 a^2 z^2-16 z^2 a^{-2} +8 z^2 a^{-4} -z^2 a^{-6} +13 z^2-2 a^2-7 a^{-2} +4 a^{-4} - a^{-6} +7 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+3 a z^9+7 z^9 a^{-1} +4 z^9 a^{-3} +3 a^2 z^8+9 z^8 a^{-2} +5 z^8 a^{-4} +7 z^8+a^3 z^7-7 a z^7-18 z^7 a^{-1} -8 z^7 a^{-3} +2 z^7 a^{-5} -12 a^2 z^6-41 z^6 a^{-2} -16 z^6 a^{-4} -37 z^6-4 a^3 z^5-4 a z^5+3 z^5 a^{-1} +z^5 a^{-3} -2 z^5 a^{-5} +15 a^2 z^4+55 z^4 a^{-2} +27 z^4 a^{-4} +4 z^4 a^{-6} +47 z^4+5 a^3 z^3+12 a z^3+11 z^3 a^{-1} +9 z^3 a^{-3} +6 z^3 a^{-5} +z^3 a^{-7} -8 a^2 z^2-33 z^2 a^{-2} -17 z^2 a^{-4} -3 z^2 a^{-6} -27 z^2-2 a^3 z-5 a z-6 z a^{-1} -5 z a^{-3} -3 z a^{-5} -z a^{-7} +2 a^2+7 a^{-2} +4 a^{-4} + a^{-6} +7 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
