K12n784
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^6+6 q^5-12 q^4+17 q^3-19 q^2+21 q-18+14 q^{-1} -9 q^{-2} +4 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+6 t^3-15 t^2+25 t-29+25 t^{-1} -15 t^{-2} +6 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-2 z^6+z^4+3 z^2+1 }[/math] |
| Determinant | 123 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -5 z^6 a^{-2} +z^6 a^{-4} +2 z^6-a^2 z^4-9 z^4 a^{-2} +4 z^4 a^{-4} +7 z^4-2 a^2 z^2-6 z^2 a^{-2} +5 z^2 a^{-4} -z^2 a^{-6} +7 z^2-a^2+ a^{-4} - a^{-6} +2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-2} +3 z^{10}+6 a z^9+15 z^9 a^{-1} +9 z^9 a^{-3} +4 a^2 z^8+10 z^8 a^{-2} +10 z^8 a^{-4} +4 z^8+a^3 z^7-17 a z^7-42 z^7 a^{-1} -19 z^7 a^{-3} +5 z^7 a^{-5} -13 a^2 z^6-48 z^6 a^{-2} -23 z^6 a^{-4} +z^6 a^{-6} -37 z^6-3 a^3 z^5+9 a z^5+28 z^5 a^{-1} +13 z^5 a^{-3} -3 z^5 a^{-5} +13 a^2 z^4+48 z^4 a^{-2} +26 z^4 a^{-4} +6 z^4 a^{-6} +41 z^4+3 a^3 z^3+3 a z^3-6 z^3 a^{-1} -5 z^3 a^{-3} +4 z^3 a^{-5} +3 z^3 a^{-7} -5 a^2 z^2-18 z^2 a^{-2} -11 z^2 a^{-4} -4 z^2 a^{-6} -16 z^2-a^3 z-a z+z a^{-1} +2 z a^{-3} -z a^{-5} -2 z a^{-7} +a^2+ a^{-4} + a^{-6} +2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
