K13n4065
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n4065/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+13 t^2-22 t+27-22 t^{-1} +13 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13n4065/Conway Polynomial |
| Determinant | 109 |
| Signature | 0 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} +6 z^6 a^{-2} -2 z^6 a^{-4} -z^6+14 z^4 a^{-2} -8 z^4 a^{-4} +z^4 a^{-6} -4 z^4+14 z^2 a^{-2} -10 z^2 a^{-4} +2 z^2 a^{-6} -5 z^2+5 a^{-2} -4 a^{-4} + a^{-6} -1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{11} a^{-3} +3 z^{11} a^{-5} +7 z^{10} a^{-2} +13 z^{10} a^{-4} +6 z^{10} a^{-6} +5 z^9 a^{-1} -3 z^9 a^{-3} -4 z^9 a^{-5} +4 z^9 a^{-7} -32 z^8 a^{-2} -61 z^8 a^{-4} -27 z^8 a^{-6} +z^8 a^{-8} +z^8-18 z^7 a^{-1} -29 z^7 a^{-3} -29 z^7 a^{-5} -18 z^7 a^{-7} +56 z^6 a^{-2} +88 z^6 a^{-4} +33 z^6 a^{-6} -4 z^6 a^{-8} +5 z^6+6 a z^5+27 z^5 a^{-1} +57 z^5 a^{-3} +59 z^5 a^{-5} +23 z^5 a^{-7} +3 a^2 z^4-55 z^4 a^{-2} -55 z^4 a^{-4} -13 z^4 a^{-6} +4 z^4 a^{-8} -14 z^4+a^3 z^3-7 a z^3-23 z^3 a^{-1} -38 z^3 a^{-3} -34 z^3 a^{-5} -11 z^3 a^{-7} -a^2 z^2+26 z^2 a^{-2} +20 z^2 a^{-4} +3 z^2 a^{-6} -z^2 a^{-8} +9 z^2+2 a z+6 z a^{-1} +9 z a^{-3} +7 z a^{-5} +2 z a^{-7} -5 a^{-2} -4 a^{-4} - a^{-6} -1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
