K13n3057
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n3057/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-7 t^3+25 t^2-50 t+63-50 t^{-1} +25 t^{-2} -7 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13n3057/Conway Polynomial |
| Determinant | 229 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8-a^2 z^6-2 z^6 a^{-2} +4 z^6-a^2 z^4-5 z^4 a^{-2} +z^4 a^{-4} +8 z^4-a^4 z^2-5 z^2 a^{-2} +z^2 a^{-4} +8 z^2-a^4-2 a^{-2} +4 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a z^{11}+3 z^{11} a^{-1} +7 a^2 z^{10}+10 z^{10} a^{-2} +17 z^{10}+5 a^3 z^9+11 a z^9+20 z^9 a^{-1} +14 z^9 a^{-3} +a^4 z^8-13 a^2 z^8-4 z^8 a^{-2} +11 z^8 a^{-4} -29 z^8-7 a^3 z^7-33 a z^7-54 z^7 a^{-1} -23 z^7 a^{-3} +5 z^7 a^{-5} +6 a^4 z^6+24 a^2 z^6-24 z^6 a^{-2} -20 z^6 a^{-4} +z^6 a^{-6} +15 z^6+3 a^5 z^5+15 a^3 z^5+39 a z^5+40 z^5 a^{-1} +5 z^5 a^{-3} -8 z^5 a^{-5} -11 a^4 z^4-21 a^2 z^4+22 z^4 a^{-2} +10 z^4 a^{-4} -z^4 a^{-6} +z^4-6 a^5 z^3-17 a^3 z^3-20 a z^3-8 z^3 a^{-1} +4 z^3 a^{-3} +3 z^3 a^{-5} +5 a^4 z^2+5 a^2 z^2-8 z^2 a^{-2} -2 z^2 a^{-4} -6 z^2+3 a^5 z+5 a^3 z+2 a z-2 z a^{-1} -2 z a^{-3} -a^4+2 a^{-2} +4 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
