K13n3581
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n3581/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^5+5 t^4-10 t^3+10 t^2-3 t-1-3 t^{-1} +10 t^{-2} -10 t^{-3} +5 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | Data:K13n3581/Conway Polynomial |
| Determinant | 57 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -7 z^8 a^{-4} +z^8 a^{-6} +5 z^6 a^{-2} -16 z^6 a^{-4} +6 z^6 a^{-6} +6 z^4 a^{-2} -14 z^4 a^{-4} +9 z^4 a^{-6} -z^4 a^{-8} +2 z^2 a^{-2} -2 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} + a^{-2} + a^{-4} - a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +6 z^{10} a^{-2} +11 z^{10} a^{-4} +5 z^{10} a^{-6} +4 z^9 a^{-1} -9 z^9 a^{-3} -11 z^9 a^{-5} +2 z^9 a^{-7} -31 z^8 a^{-2} -62 z^8 a^{-4} -30 z^8 a^{-6} +z^8-19 z^7 a^{-1} -15 z^7 a^{-3} -8 z^7 a^{-5} -12 z^7 a^{-7} +42 z^6 a^{-2} +97 z^6 a^{-4} +51 z^6 a^{-6} -4 z^6+22 z^5 a^{-1} +45 z^5 a^{-3} +40 z^5 a^{-5} +17 z^5 a^{-7} -17 z^4 a^{-2} -49 z^4 a^{-4} -34 z^4 a^{-6} -5 z^4 a^{-8} +3 z^4-8 z^3 a^{-1} -24 z^3 a^{-3} -26 z^3 a^{-5} -12 z^3 a^{-7} -2 z^3 a^{-9} +z^2 a^{-2} +5 z^2 a^{-4} +6 z^2 a^{-6} +3 z^2 a^{-8} -z^2+z a^{-1} +4 z a^{-3} +4 z a^{-5} +2 z a^{-7} +z a^{-9} - a^{-2} + a^{-4} + a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
