K12n637
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-5 q^8+11 q^7-16 q^6+21 q^5-23 q^4+21 q^3-18 q^2+12 q-5+2 q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+32 t-41+32 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4-2 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ 2 z^6 a^{-4} -4 z^4 a^{-2} +6 z^4 a^{-4} -3 z^4 a^{-6} -8 z^2 a^{-2} +7 z^2 a^{-4} -4 z^2 a^{-6} +z^2 a^{-8} +2 z^2-4 a^{-2} +2 a^{-4} +3 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 3 z^{10} a^{-4} +3 z^{10} a^{-6} +6 z^9 a^{-3} +15 z^9 a^{-5} +9 z^9 a^{-7} +4 z^8 a^{-2} +5 z^8 a^{-4} +11 z^8 a^{-6} +10 z^8 a^{-8} +z^7 a^{-1} -13 z^7 a^{-3} -35 z^7 a^{-5} -16 z^7 a^{-7} +5 z^7 a^{-9} -7 z^6 a^{-2} -24 z^6 a^{-4} -41 z^6 a^{-6} -23 z^6 a^{-8} +z^6 a^{-10} +3 z^5 a^{-1} +18 z^5 a^{-3} +25 z^5 a^{-5} +z^5 a^{-7} -9 z^5 a^{-9} +17 z^4 a^{-2} +31 z^4 a^{-4} +29 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +3 z^4-3 z^3 a^{-1} -2 z^3 a^{-3} +z^3 a^{-7} +2 z^3 a^{-9} -15 z^2 a^{-2} -11 z^2 a^{-4} -3 z^2 a^{-6} -z^2 a^{-8} -6 z^2-z a^{-1} -5 z a^{-3} -5 z a^{-5} -z a^{-7} +4 a^{-2} +2 a^{-4} +3 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
