K12a851
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^9-3 q^8+6 q^7-12 q^6+18 q^5-23 q^4+26 q^3-24 q^2+21 q-15+9 q^{-1} -4 q^{-2} + q^{-3} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+9 t^3-20 t^2+32 t-37+32 t^{-1} -20 t^{-2} +9 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-7 z^6-6 z^4+z^2+1 }[/math] |
| Determinant | 163 |
| 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^6-4 z^4 a^{-2} -9 z^4 a^{-4} +4 z^4 a^{-6} +3 z^4+z^2 a^{-2} -6 z^2 a^{-4} +4 z^2 a^{-6} +2 z^2+2 a^{-2} - a^{-4} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-3} +2 z^{11} a^{-5} +6 z^{10} a^{-2} +10 z^{10} a^{-4} +4 z^{10} a^{-6} +9 z^9 a^{-1} +6 z^9 a^{-3} +z^9 a^{-5} +4 z^9 a^{-7} -10 z^8 a^{-2} -30 z^8 a^{-4} -8 z^8 a^{-6} +4 z^8 a^{-8} +8 z^8+4 a z^7-23 z^7 a^{-1} -24 z^7 a^{-3} -4 z^7 a^{-5} -4 z^7 a^{-7} +3 z^7 a^{-9} +a^2 z^6+3 z^6 a^{-2} +50 z^6 a^{-4} +16 z^6 a^{-6} -8 z^6 a^{-8} +z^6 a^{-10} -21 z^6-9 a z^5+19 z^5 a^{-1} +31 z^5 a^{-3} +6 z^5 a^{-5} -6 z^5 a^{-7} -9 z^5 a^{-9} -2 a^2 z^4+z^4 a^{-2} -41 z^4 a^{-4} -20 z^4 a^{-6} +2 z^4 a^{-8} -3 z^4 a^{-10} +15 z^4+3 a z^3-7 z^3 a^{-1} -14 z^3 a^{-3} -2 z^3 a^{-5} +10 z^3 a^{-7} +8 z^3 a^{-9} +3 z^2 a^{-2} +15 z^2 a^{-4} +8 z^2 a^{-6} +2 z^2 a^{-8} +2 z^2 a^{-10} -4 z^2+z a^{-1} +2 z a^{-3} -2 z a^{-5} -5 z a^{-7} -2 z a^{-9} -2 a^{-2} - a^{-4} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
