K12a597
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^5-3 q^4+6 q^3-9 q^2+14 q-17+18 q^{-1} -18 q^{-2} +15 q^{-3} -11 q^{-4} +7 q^{-5} -3 q^{-6} + q^{-7} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 2 t^3-13 t^2+29 t-35+29 t^{-1} -13 t^{-2} +2 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 2 z^6-z^4-5 z^2+1 }[/math] |
| Determinant | 123 |
| Signature | -2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^2 a^6+a^6-2 z^4 a^4-3 z^2 a^4+z^6 a^2+z^4 a^2-2 z^2 a^2-2 a^2+z^6+2 z^4+2 z^2+2-2 z^4 a^{-2} -4 z^2 a^{-2} - a^{-2} +z^2 a^{-4} + a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+6 a^3 z^9+7 a z^9+4 z^9 a^{-1} +3 z^9 a^{-3} +8 a^4 z^8+4 a^2 z^8-11 z^8 a^{-2} +z^8 a^{-4} -16 z^8+8 a^5 z^7-6 a^3 z^7-28 a z^7-29 z^7 a^{-1} -15 z^7 a^{-3} +6 a^6 z^6-11 a^4 z^6-28 a^2 z^6+6 z^6 a^{-2} -5 z^6 a^{-4} +3 a^7 z^5-11 a^5 z^5-5 a^3 z^5+26 a z^5+40 z^5 a^{-1} +23 z^5 a^{-3} +a^8 z^4-7 a^6 z^4+4 a^4 z^4+29 a^2 z^4+11 z^4 a^{-2} +8 z^4 a^{-4} +20 z^4-2 a^7 z^3+8 a^5 z^3+2 a^3 z^3-13 a z^3-16 z^3 a^{-1} -11 z^3 a^{-3} -a^8 z^2+5 a^6 z^2-15 a^2 z^2-9 z^2 a^{-2} -5 z^2 a^{-4} -13 z^2-2 a^5 z+a^3 z+4 a z+2 z a^{-1} +z a^{-3} -a^6+2 a^2+ a^{-2} + a^{-4} +2 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
