K12n43
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ 2 q^4-4 q^3+7 q^2-11 q+13-13 q^{-1} +12 q^{-2} -9 q^{-3} +6 q^{-4} -3 q^{-5} + q^{-6} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+10 t^2-15 t+19-15 t^{-1} +10 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6-4 z^2+1 }[/math] |
| Determinant | 81 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-2 a^2 z^6-z^6 a^{-2} +6 z^6+a^4 z^4-9 a^2 z^4-5 z^4 a^{-2} +13 z^4+3 a^4 z^2-12 a^2 z^2-8 z^2 a^{-2} +z^2 a^{-4} +12 z^2+2 a^4-4 a^2-4 a^{-2} +2 a^{-4} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^2 z^{10}+z^{10}+3 a^3 z^9+6 a z^9+3 z^9 a^{-1} +4 a^4 z^8+5 a^2 z^8+3 z^8 a^{-2} +4 z^8+3 a^5 z^7-5 a^3 z^7-18 a z^7-9 z^7 a^{-1} +z^7 a^{-3} +a^6 z^6-11 a^4 z^6-24 a^2 z^6-10 z^6 a^{-2} -22 z^6-9 a^5 z^5-2 a^3 z^5+20 a z^5+14 z^5 a^{-1} +z^5 a^{-3} -3 a^6 z^4+8 a^4 z^4+34 a^2 z^4+20 z^4 a^{-2} +3 z^4 a^{-4} +40 z^4+6 a^5 z^3+2 a^3 z^3-4 a z^3-5 z^3 a^{-1} -5 z^3 a^{-3} +2 a^6 z^2-6 a^4 z^2-21 a^2 z^2-17 z^2 a^{-2} -7 z^2 a^{-4} -23 z^2-a^5 z-a^3 z-a z+z a^{-1} +2 z a^{-3} +2 a^4+4 a^2+4 a^{-2} +2 a^{-4} +5 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
