K13a3491
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13a3491/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 6 t^3-33 t^2+76 t-97+76 t^{-1} -33 t^{-2} +6 t^{-3} }[/math] |
| Conway polynomial | Data:K13a3491/Conway Polynomial |
| Determinant | 327 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^8+a^8-3 z^4 a^6-4 z^2 a^6-2 a^6+2 z^6 a^4+2 z^4 a^4+z^2 a^4+2 a^4+3 z^6 a^2+5 z^4 a^2+z^2 a^2-2 a^2+z^6+2-z^4 a^{-2} -z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 a^4 z^{12}+3 a^2 z^{12}+9 a^5 z^{11}+18 a^3 z^{11}+9 a z^{11}+13 a^6 z^{10}+18 a^4 z^{10}+16 a^2 z^{10}+11 z^{10}+13 a^7 z^9-2 a^5 z^9-39 a^3 z^9-16 a z^9+8 z^9 a^{-1} +9 a^8 z^8-15 a^6 z^8-54 a^4 z^8-64 a^2 z^8+4 z^8 a^{-2} -30 z^8+4 a^9 z^7-21 a^7 z^7-19 a^5 z^7+33 a^3 z^7+4 a z^7-22 z^7 a^{-1} +z^7 a^{-3} +a^{10} z^6-16 a^8 z^6-5 a^6 z^6+55 a^4 z^6+84 a^2 z^6-12 z^6 a^{-2} +29 z^6-7 a^9 z^5+11 a^7 z^5+17 a^5 z^5-18 a^3 z^5+3 a z^5+17 z^5 a^{-1} -3 z^5 a^{-3} -2 a^{10} z^4+11 a^8 z^4+15 a^6 z^4-21 a^4 z^4-47 a^2 z^4+10 z^4 a^{-2} -14 z^4+4 a^9 z^3-3 a^7 z^3+15 a^3 z^3+a z^3-5 z^3 a^{-1} +2 z^3 a^{-3} +a^{10} z^2-5 a^8 z^2-10 a^6 z^2+6 a^2 z^2-3 z^2 a^{-2} -z^2-a^9 z-a^7 z-3 a^5 z-5 a^3 z-2 a z+a^8+2 a^6+2 a^4+2 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. |
