K12n537
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^6+5 q^5-10 q^4+15 q^3-18 q^2+19 q-18+14 q^{-1} -9 q^{-2} +5 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-12 t^2+27 t-33+27 t^{-1} -12 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-3 z^2+1 }[/math] |
| Determinant | 115 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +z^6-a^2 z^4+z^4 a^{-2} -z^4 a^{-4} +z^4-z^2 a^{-2} -2 z^2+2 a^2+ a^{-4} -2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{10} a^{-2} +4 z^{10}+8 a z^9+17 z^9 a^{-1} +9 z^9 a^{-3} +5 a^2 z^8+7 z^8 a^{-4} -2 z^8+a^3 z^7-28 a z^7-59 z^7 a^{-1} -28 z^7 a^{-3} +2 z^7 a^{-5} -16 a^2 z^6-28 z^6 a^{-2} -17 z^6 a^{-4} -27 z^6-2 a^3 z^5+26 a z^5+61 z^5 a^{-1} +36 z^5 a^{-3} +3 z^5 a^{-5} +11 a^2 z^4+34 z^4 a^{-2} +22 z^4 a^{-4} +5 z^4 a^{-6} +28 z^4-7 a z^3-26 z^3 a^{-1} -22 z^3 a^{-3} -2 z^3 a^{-5} +z^3 a^{-7} +2 a^2 z^2-13 z^2 a^{-2} -11 z^2 a^{-4} -2 z^2 a^{-6} -2 z^2+4 z a^{-1} +5 z a^{-3} +z a^{-5} -2 a^2+ a^{-4} -2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
