K13n3787
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Data:K13n3787/Jones Polynomial |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-20 t^2+34 t-41+34 t^{-1} -20 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | Data:K13n3787/Conway Polynomial |
| Determinant | 171 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -z^8 a^{-4} -4 z^6 a^{-2} -5 z^6 a^{-4} +z^6 a^{-6} +z^6-5 z^4 a^{-2} -9 z^4 a^{-4} +5 z^4 a^{-6} +3 z^4-2 z^2 a^{-2} -5 z^2 a^{-4} +8 z^2 a^{-6} -z^2 a^{-8} +3 z^2- a^{-2} +3 a^{-6} -2 a^{-8} +1 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +11 z^{10} a^{-4} +5 z^{10} a^{-6} +9 z^9 a^{-1} +10 z^9 a^{-3} +5 z^9 a^{-5} +4 z^9 a^{-7} -3 z^8 a^{-2} -28 z^8 a^{-4} -16 z^8 a^{-6} +z^8 a^{-8} +8 z^8+4 a z^7-16 z^7 a^{-1} -34 z^7 a^{-3} -27 z^7 a^{-5} -13 z^7 a^{-7} +a^2 z^6-16 z^6 a^{-2} +31 z^6 a^{-4} +31 z^6 a^{-6} +2 z^6 a^{-8} -17 z^6-8 a z^5+4 z^5 a^{-1} +38 z^5 a^{-3} +52 z^5 a^{-5} +29 z^5 a^{-7} +3 z^5 a^{-9} -2 a^2 z^4+18 z^4 a^{-2} -9 z^4 a^{-4} -23 z^4 a^{-6} -8 z^4 a^{-8} +10 z^4+4 a z^3-z^3 a^{-1} -18 z^3 a^{-3} -36 z^3 a^{-5} -32 z^3 a^{-7} -9 z^3 a^{-9} +a^2 z^2-8 z^2 a^{-2} +7 z^2 a^{-6} +5 z^2 a^{-8} -5 z^2-a z+5 z a^{-3} +9 z a^{-5} +11 z a^{-7} +6 z a^{-9} + a^{-2} -3 a^{-6} -2 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. |
