K13n2545
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n2545/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -t^5+4 t^4-7 t^3+7 t^2-3 t+1-3 t^{-1} +7 t^{-2} -7 t^{-3} +4 t^{-4} - t^{-5} }[/math] |
| Conway polynomial | Data:K13n2545/Conway Polynomial |
| Determinant | 45 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^{10} a^{-4} +z^8 a^{-2} -8 z^8 a^{-4} +z^8 a^{-6} +6 z^6 a^{-2} -23 z^6 a^{-4} +7 z^6 a^{-6} +11 z^4 a^{-2} -30 z^4 a^{-4} +15 z^4 a^{-6} -z^4 a^{-8} +8 z^2 a^{-2} -17 z^2 a^{-4} +12 z^2 a^{-6} -2 z^2 a^{-8} +3 a^{-2} -4 a^{-4} +3 a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +7 z^{10} a^{-4} +3 z^{10} a^{-6} +3 z^9 a^{-1} -8 z^9 a^{-3} -10 z^9 a^{-5} +z^9 a^{-7} -23 z^8 a^{-2} -44 z^8 a^{-4} -20 z^8 a^{-6} +z^8-16 z^7 a^{-1} +z^7 a^{-3} +11 z^7 a^{-5} -6 z^7 a^{-7} +41 z^6 a^{-2} +91 z^6 a^{-4} +45 z^6 a^{-6} -5 z^6+23 z^5 a^{-1} +15 z^5 a^{-3} +z^5 a^{-5} +9 z^5 a^{-7} -32 z^4 a^{-2} -84 z^4 a^{-4} -49 z^4 a^{-6} -3 z^4 a^{-8} +6 z^4-9 z^3 a^{-1} -12 z^3 a^{-3} -8 z^3 a^{-5} -6 z^3 a^{-7} -z^3 a^{-9} +13 z^2 a^{-2} +32 z^2 a^{-4} +23 z^2 a^{-6} +5 z^2 a^{-8} -z^2+z a^{-1} +3 z a^{-3} +3 z a^{-5} +2 z a^{-7} +z a^{-9} -3 a^{-2} -4 a^{-4} -3 a^{-6} - a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
