K12n517
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^5+5 q^4-9 q^3+14 q^2-16 q+17-15 q^{-1} +12 q^{-2} -7 q^{-3} +3 q^{-4} - q^{-5} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-4 t^3+11 t^2-21 t+27-21 t^{-1} +11 t^{-2} -4 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+4 z^6+7 z^4+3 z^2+1 }[/math] |
| Determinant | 101 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-z^6 a^{-2} +6 z^6-4 a^2 z^4-3 z^4 a^{-2} +14 z^4-6 a^2 z^2-3 z^2 a^{-2} -z^2 a^{-4} +13 z^2-2 a^2- a^{-4} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10}+4 a z^9+6 z^9 a^{-1} +2 z^9 a^{-3} +6 a^2 z^8+4 z^8 a^{-2} +z^8 a^{-4} +9 z^8+5 a^3 z^7-2 a z^7-9 z^7 a^{-1} -2 z^7 a^{-3} +3 a^4 z^6-10 a^2 z^6-10 z^6 a^{-2} +2 z^6 a^{-4} -25 z^6+a^5 z^5-7 a^3 z^5-3 a z^5+5 z^5 a^{-1} +3 z^5 a^{-3} +3 z^5 a^{-5} -5 a^4 z^4+10 a^2 z^4+8 z^4 a^{-2} -8 z^4 a^{-4} +31 z^4-2 a^5 z^3+2 a^3 z^3+4 a z^3-z^3 a^{-1} -8 z^3 a^{-3} -7 z^3 a^{-5} +2 a^4 z^2-8 a^2 z^2-3 z^2 a^{-2} +5 z^2 a^{-4} -18 z^2+a^5 z-2 a z+4 z a^{-3} +3 z a^{-5} +2 a^2- a^{-4} +4 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
