K12a882
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^4+3 q^3-7 q^2+12 q-17+22 q^{-1} -22 q^{-2} +22 q^{-3} -18 q^{-4} +12 q^{-5} -7 q^{-6} +3 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 4 t^3-16 t^2+33 t-41+33 t^{-1} -16 t^{-2} +4 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 4 z^6+8 z^4+5 z^2+1 }[/math] |
| Determinant | 147 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-2 z^2 a^6-a^6+z^6 a^4+2 z^4 a^4+z^2 a^4-a^4+2 z^6 a^2+6 z^4 a^2+7 z^2 a^2+4 a^2+z^6+2 z^4+z^2-z^4 a^{-2} -2 z^2 a^{-2} - a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^3 z^{11}+a z^{11}+4 a^4 z^{10}+7 a^2 z^{10}+3 z^{10}+7 a^5 z^9+10 a^3 z^9+7 a z^9+4 z^9 a^{-1} +8 a^6 z^8-a^4 z^8-15 a^2 z^8+3 z^8 a^{-2} -3 z^8+6 a^7 z^7-13 a^5 z^7-33 a^3 z^7-26 a z^7-11 z^7 a^{-1} +z^7 a^{-3} +3 a^8 z^6-19 a^6 z^6-10 a^4 z^6+14 a^2 z^6-11 z^6 a^{-2} -9 z^6+a^9 z^5-13 a^7 z^5+9 a^5 z^5+45 a^3 z^5+31 a z^5+5 z^5 a^{-1} -4 z^5 a^{-3} -5 a^8 z^4+21 a^6 z^4+15 a^4 z^4-14 a^2 z^4+12 z^4 a^{-2} +9 z^4-2 a^9 z^3+11 a^7 z^3+5 a^5 z^3-32 a^3 z^3-26 a z^3+3 z^3 a^{-1} +5 z^3 a^{-3} -7 a^6 z^2-3 a^4 z^2+6 a^2 z^2-4 z^2 a^{-2} -2 z^2-4 a^7 z-a^5 z+9 a^3 z+8 a z-2 z a^{-3} +a^6-a^4-4 a^2+ a^{-2} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
