K13n1511
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n1511/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^4-6 t^3+13 t^2-14 t+13-14 t^{-1} +13 t^{-2} -6 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | Data:K13n1511/Conway Polynomial |
| Determinant | 81 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -2 z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -8 z^4 a^{-2} +8 z^4 a^{-4} -4 z^4 a^{-6} +z^4-7 z^2 a^{-2} +7 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} +3 z^2- a^{-2} +3 a^{-4} -3 a^{-6} + a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-3} +z^{11} a^{-5} +3 z^{10} a^{-2} +6 z^{10} a^{-4} +3 z^{10} a^{-6} +3 z^9 a^{-1} +4 z^9 a^{-3} +4 z^9 a^{-5} +3 z^9 a^{-7} -11 z^8 a^{-2} -23 z^8 a^{-4} -10 z^8 a^{-6} +z^8 a^{-8} +z^8-15 z^7 a^{-1} -35 z^7 a^{-3} -32 z^7 a^{-5} -12 z^7 a^{-7} +4 z^6 a^{-2} +18 z^6 a^{-4} +7 z^6 a^{-6} -2 z^6 a^{-8} -5 z^6+23 z^5 a^{-1} +55 z^5 a^{-3} +49 z^5 a^{-5} +18 z^5 a^{-7} +z^5 a^{-9} +12 z^4 a^{-2} +2 z^4 a^{-4} +z^4 a^{-6} +3 z^4 a^{-8} +8 z^4-13 z^3 a^{-1} -30 z^3 a^{-3} -29 z^3 a^{-5} -10 z^3 a^{-7} +2 z^3 a^{-9} -8 z^2 a^{-2} -5 z^2 a^{-4} -5 z^2 a^{-6} -z^2 a^{-8} +2 z^2 a^{-10} -5 z^2+2 z a^{-1} +6 z a^{-3} +4 z a^{-5} -2 z a^{-7} -2 z a^{-9} + a^{-2} +3 a^{-4} +3 a^{-6} + a^{-8} +1 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
