K13n41
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n41/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^3-14 t^2+48 t-69+48 t^{-1} -14 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | Data:K13n41/Conway Polynomial |
| Determinant | 195 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -2 a^8+6 z^2 a^6+4 a^6-5 z^4 a^4-5 z^2 a^4-a^4+z^6 a^2-z^4 a^2-2 z^2 a^2-2 a^2-2 z^4+z^2+2+z^2 a^{-2} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 a^5 z^{11}+2 a^3 z^{11}+5 a^6 z^{10}+12 a^4 z^{10}+7 a^2 z^{10}+4 a^7 z^9+9 a^5 z^9+16 a^3 z^9+11 a z^9+a^8 z^8-10 a^6 z^8-20 a^4 z^8+9 z^8-8 a^7 z^7-29 a^5 z^7-46 a^3 z^7-21 a z^7+4 z^7 a^{-1} +4 a^8 z^6+21 a^6 z^6+10 a^4 z^6-27 a^2 z^6+z^6 a^{-2} -19 z^6+3 a^9 z^5+19 a^7 z^5+43 a^5 z^5+48 a^3 z^5+14 a z^5-7 z^5 a^{-1} -10 a^8 z^4-22 a^6 z^4+2 a^4 z^4+31 a^2 z^4-2 z^4 a^{-2} +15 z^4-7 a^9 z^3-23 a^7 z^3-30 a^5 z^3-28 a^3 z^3-11 a z^3+3 z^3 a^{-1} +6 a^8 z^2+12 a^6 z^2-16 a^2 z^2+z^2 a^{-2} -9 z^2+4 a^9 z+8 a^7 z+9 a^5 z+9 a^3 z+4 a z-2 a^8-4 a^6-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. |
