K12n500
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^2+2 q-4+7 q^{-1} -7 q^{-2} +9 q^{-3} -8 q^{-4} +6 q^{-5} -4 q^{-6} +2 q^{-7} - q^{-8} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-6 t^2+11 t-13+11 t^{-1} -6 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6+6 z^4+5 z^2+1 }[/math] |
| Determinant | 51 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^4 a^6-3 z^2 a^6-2 a^6+z^6 a^4+4 z^4 a^4+5 z^2 a^4+a^4+z^6 a^2+4 z^4 a^2+6 z^2 a^2+4 a^2-z^4-3 z^2-2 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a^4 z^{10}+a^2 z^{10}+2 a^5 z^9+3 a^3 z^9+a z^9+3 a^6 z^8-3 a^4 z^8-6 a^2 z^8+3 a^7 z^7-6 a^5 z^7-15 a^3 z^7-6 a z^7+2 a^8 z^6-10 a^6 z^6+4 a^4 z^6+18 a^2 z^6+2 z^6+a^9 z^5-9 a^7 z^5+6 a^5 z^5+34 a^3 z^5+19 a z^5+z^5 a^{-1} -5 a^8 z^4+13 a^6 z^4+3 a^4 z^4-21 a^2 z^4-6 z^4-3 a^9 z^3+8 a^7 z^3+4 a^5 z^3-29 a^3 z^3-26 a z^3-4 z^3 a^{-1} +a^8 z^2-6 a^6 z^2-3 a^4 z^2+9 a^2 z^2+5 z^2+a^9 z-3 a^7 z-2 a^5 z+8 a^3 z+10 a z+4 z a^{-1} +2 a^6+a^4-4 a^2-2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
