K13n4055
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n4055/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ 2 t^4-9 t^3+19 t^2-25 t+27-25 t^{-1} +19 t^{-2} -9 t^{-3} +2 t^{-4} }[/math] |
| Conway polynomial | Data:K13n4055/Conway Polynomial |
| Determinant | 137 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} +z^8 a^{-6} -z^6 a^{-2} +4 z^6 a^{-4} +5 z^6 a^{-6} -z^6 a^{-8} -3 z^4 a^{-2} +4 z^4 a^{-4} +9 z^4 a^{-6} -5 z^4 a^{-8} -z^2 a^{-2} +z^2 a^{-4} +8 z^2 a^{-6} -7 z^2 a^{-8} +z^2 a^{-10} + a^{-2} +2 a^{-6} -3 a^{-8} + a^{-10} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-5} +2 z^{11} a^{-7} +5 z^{10} a^{-4} +9 z^{10} a^{-6} +4 z^{10} a^{-8} +6 z^9 a^{-3} +2 z^9 a^{-5} -z^9 a^{-7} +3 z^9 a^{-9} +4 z^8 a^{-2} -12 z^8 a^{-4} -29 z^8 a^{-6} -12 z^8 a^{-8} +z^8 a^{-10} +z^7 a^{-1} -19 z^7 a^{-3} -15 z^7 a^{-5} -5 z^7 a^{-9} -14 z^6 a^{-2} +4 z^6 a^{-4} +43 z^6 a^{-6} +28 z^6 a^{-8} +3 z^6 a^{-10} -3 z^5 a^{-1} +14 z^5 a^{-3} +7 z^5 a^{-5} -3 z^5 a^{-7} +11 z^5 a^{-9} +4 z^5 a^{-11} +13 z^4 a^{-2} -2 z^4 a^{-4} -42 z^4 a^{-6} -30 z^4 a^{-8} -2 z^4 a^{-10} +z^4 a^{-12} +2 z^3 a^{-1} -z^3 a^{-3} +3 z^3 a^{-5} +4 z^3 a^{-7} -6 z^3 a^{-9} -4 z^3 a^{-11} -2 z^2 a^{-2} +3 z^2 a^{-4} +18 z^2 a^{-6} +16 z^2 a^{-8} +2 z^2 a^{-10} -z^2 a^{-12} -3 z a^{-5} -3 z a^{-7} +z a^{-9} +z a^{-11} - a^{-2} -2 a^{-6} -3 a^{-8} - a^{-10} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
