K12n229
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -2 q^{10}+4 q^9-6 q^8+8 q^7-8 q^6+8 q^5-7 q^4+5 q^3-2 q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+5 t^3-8 t^2+8 t-7+8 t^{-1} -8 t^{-2} +5 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-3 z^6+2 z^4+5 z^2+1 }[/math] |
| Determinant | 51 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} +z^6 a^{-4} -6 z^6 a^{-6} +2 z^6 a^{-8} +5 z^4 a^{-4} -13 z^4 a^{-6} +11 z^4 a^{-8} -z^4 a^{-10} +8 z^2 a^{-4} -15 z^2 a^{-6} +18 z^2 a^{-8} -6 z^2 a^{-10} +4 a^{-4} -8 a^{-6} +10 a^{-8} -6 a^{-10} + a^{-12} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-6} +z^{10} a^{-8} +2 z^9 a^{-5} +6 z^9 a^{-7} +4 z^9 a^{-9} +z^8 a^{-4} +z^8 a^{-6} +6 z^8 a^{-8} +6 z^8 a^{-10} -10 z^7 a^{-5} -26 z^7 a^{-7} -13 z^7 a^{-9} +3 z^7 a^{-11} -6 z^6 a^{-4} -24 z^6 a^{-6} -47 z^6 a^{-8} -29 z^6 a^{-10} +15 z^5 a^{-5} +27 z^5 a^{-7} -z^5 a^{-9} -13 z^5 a^{-11} +13 z^4 a^{-4} +48 z^4 a^{-6} +77 z^4 a^{-8} +43 z^4 a^{-10} +z^4 a^{-12} -7 z^3 a^{-5} -5 z^3 a^{-7} +18 z^3 a^{-9} +16 z^3 a^{-11} -12 z^2 a^{-4} -34 z^2 a^{-6} -47 z^2 a^{-8} -27 z^2 a^{-10} -2 z^2 a^{-12} -z a^{-7} -7 z a^{-9} -6 z a^{-11} +4 a^{-4} +8 a^{-6} +10 a^{-8} +6 a^{-10} + a^{-12} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
