K12n467
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-2 q^8+3 q^7-5 q^6+6 q^5-7 q^4+7 q^3-5 q^2+4 q-2+ q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+3 t^3-5 t^2+8 t-9+8 t^{-1} -5 t^{-2} +3 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8-5 z^6-7 z^4-z^2+1 }[/math] |
| Determinant | 43 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-4} +z^6 a^{-2} -7 z^6 a^{-4} +z^6 a^{-6} +5 z^4 a^{-2} -17 z^4 a^{-4} +5 z^4 a^{-6} +8 z^2 a^{-2} -16 z^2 a^{-4} +7 z^2 a^{-6} +4 a^{-2} -5 a^{-4} +2 a^{-6} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{10} a^{-4} +z^{10} a^{-6} +z^9 a^{-3} +3 z^9 a^{-5} +2 z^9 a^{-7} -6 z^8 a^{-4} -4 z^8 a^{-6} +2 z^8 a^{-8} -5 z^7 a^{-3} -16 z^7 a^{-5} -9 z^7 a^{-7} +2 z^7 a^{-9} +3 z^6 a^{-2} +18 z^6 a^{-4} +7 z^6 a^{-6} -7 z^6 a^{-8} +z^6 a^{-10} +2 z^5 a^{-1} +13 z^5 a^{-3} +34 z^5 a^{-5} +15 z^5 a^{-7} -8 z^5 a^{-9} -8 z^4 a^{-2} -25 z^4 a^{-4} -7 z^4 a^{-6} +5 z^4 a^{-8} -4 z^4 a^{-10} +z^4-4 z^3 a^{-1} -12 z^3 a^{-3} -27 z^3 a^{-5} -12 z^3 a^{-7} +7 z^3 a^{-9} +9 z^2 a^{-2} +20 z^2 a^{-4} +5 z^2 a^{-6} -z^2 a^{-8} +3 z^2 a^{-10} -2 z^2+z a^{-1} +5 z a^{-3} +7 z a^{-5} +2 z a^{-7} -z a^{-9} -4 a^{-2} -5 a^{-4} -2 a^{-6} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
