K13n1306
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n1306/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ t^3-3 t^2+6 t-7+6 t^{-1} -3 t^{-2} + t^{-3} }[/math] |
| Conway polynomial | Data:K13n1306/Conway Polynomial |
| Determinant | 27 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-2} -z^8 a^{-4} +9 z^6 a^{-2} -8 z^6 a^{-4} +z^6 a^{-6} -z^6+28 z^4 a^{-2} -24 z^4 a^{-4} +5 z^4 a^{-6} -6 z^4+37 z^2 a^{-2} -31 z^2 a^{-4} +8 z^2 a^{-6} -11 z^2+18 a^{-2} -15 a^{-4} +4 a^{-6} -6 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-2} +z^{10} a^{-4} +z^{10} a^{-6} +z^{10}+a z^9+2 z^9 a^{-1} +2 z^9 a^{-3} +3 z^9 a^{-5} +2 z^9 a^{-7} -10 z^8 a^{-2} -8 z^8 a^{-4} -4 z^8 a^{-6} +2 z^8 a^{-8} -8 z^8-8 a z^7-18 z^7 a^{-1} -19 z^7 a^{-3} -20 z^7 a^{-5} -9 z^7 a^{-7} +2 z^7 a^{-9} +33 z^6 a^{-2} +24 z^6 a^{-4} +4 z^6 a^{-6} -7 z^6 a^{-8} +z^6 a^{-10} +21 z^6+21 a z^5+51 z^5 a^{-1} +58 z^5 a^{-3} +49 z^5 a^{-5} +13 z^5 a^{-7} -8 z^5 a^{-9} -51 z^4 a^{-2} -36 z^4 a^{-4} -z^4 a^{-6} +4 z^4 a^{-8} -4 z^4 a^{-10} -24 z^4-21 a z^3-56 z^3 a^{-1} -69 z^3 a^{-3} -50 z^3 a^{-5} -9 z^3 a^{-7} +7 z^3 a^{-9} +44 z^2 a^{-2} +35 z^2 a^{-4} +4 z^2 a^{-6} +3 z^2 a^{-10} +16 z^2+7 a z+21 z a^{-1} +30 z a^{-3} +20 z a^{-5} +2 z a^{-7} -2 z a^{-9} -18 a^{-2} -15 a^{-4} -4 a^{-6} -6 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
