K13n1683
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n1683/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -4 t^2+16 t-23+16 t^{-1} -4 t^{-2} }[/math] |
| Conway polynomial | Data:K13n1683/Conway Polynomial |
| Determinant | 63 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^6 a^{-2} +z^6 a^{-6} -6 z^4 a^{-2} -2 z^4 a^{-4} +4 z^4 a^{-6} -z^4 a^{-8} +z^4-8 z^2 a^{-2} -2 z^2 a^{-4} +8 z^2 a^{-6} -2 z^2 a^{-8} +4 z^2-4 a^{-2} +4 a^{-6} -2 a^{-8} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-5} +z^{11} a^{-7} +z^{10} a^{-4} +4 z^{10} a^{-6} +3 z^{10} a^{-8} +z^9 a^{-1} -5 z^9 a^{-5} +4 z^9 a^{-9} +z^8 a^{-2} -7 z^8 a^{-4} -20 z^8 a^{-6} -10 z^8 a^{-8} +3 z^8 a^{-10} +z^8-7 z^7 a^{-1} -3 z^7 a^{-3} +10 z^7 a^{-5} -10 z^7 a^{-7} -15 z^7 a^{-9} +z^7 a^{-11} -12 z^6 a^{-2} +15 z^6 a^{-4} +40 z^6 a^{-6} +8 z^6 a^{-8} -12 z^6 a^{-10} -7 z^6+13 z^5 a^{-1} +8 z^5 a^{-3} -10 z^5 a^{-5} +12 z^5 a^{-7} +13 z^5 a^{-9} -4 z^5 a^{-11} +30 z^4 a^{-2} -8 z^4 a^{-4} -43 z^4 a^{-6} -8 z^4 a^{-8} +12 z^4 a^{-10} +15 z^4-8 z^3 a^{-1} -2 z^3 a^{-3} +7 z^3 a^{-5} -6 z^3 a^{-7} -3 z^3 a^{-9} +4 z^3 a^{-11} -22 z^2 a^{-2} +z^2 a^{-4} +21 z^2 a^{-6} +7 z^2 a^{-8} -3 z^2 a^{-10} -12 z^2+2 z a^{-1} +z a^{-3} -2 z a^{-5} -z a^{-11} +4 a^{-2} -4 a^{-6} -2 a^{-8} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
