K12n791
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^9+3 q^8-8 q^7+12 q^6-14 q^5+16 q^4-14 q^3+12 q^2-8 q+4- q^{-1} }[/math] |
| Alexander polynomial | [math]\displaystyle{ t^4-5 t^3+13 t^2-18 t+19-18 t^{-1} +13 t^{-2} -5 t^{-3} + t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ z^8+3 z^6+3 z^4+5 z^2+1 }[/math] |
| Determinant | 93 |
| Signature | 4 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^8 a^{-4} -z^6 a^{-2} +5 z^6 a^{-4} -z^6 a^{-6} -3 z^4 a^{-2} +9 z^4 a^{-4} -3 z^4 a^{-6} -2 z^2 a^{-2} +9 z^2 a^{-4} -2 z^2 a^{-6} - a^{-2} +4 a^{-4} - a^{-6} - a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{10} a^{-4} +2 z^{10} a^{-6} +5 z^9 a^{-3} +10 z^9 a^{-5} +5 z^9 a^{-7} +4 z^8 a^{-2} +5 z^8 a^{-4} +5 z^8 a^{-6} +4 z^8 a^{-8} +z^7 a^{-1} -14 z^7 a^{-3} -29 z^7 a^{-5} -13 z^7 a^{-7} +z^7 a^{-9} -14 z^6 a^{-2} -37 z^6 a^{-4} -33 z^6 a^{-6} -10 z^6 a^{-8} -3 z^5 a^{-1} +3 z^5 a^{-3} +15 z^5 a^{-5} +11 z^5 a^{-7} +2 z^5 a^{-9} +14 z^4 a^{-2} +43 z^4 a^{-4} +40 z^4 a^{-6} +14 z^4 a^{-8} +3 z^4 a^{-10} +3 z^3 a^{-1} +8 z^3 a^{-3} +5 z^3 a^{-5} -2 z^3 a^{-7} -z^3 a^{-9} +z^3 a^{-11} -5 z^2 a^{-2} -20 z^2 a^{-4} -17 z^2 a^{-6} -4 z^2 a^{-8} -2 z^2 a^{-10} -z a^{-1} -3 z a^{-3} -4 z a^{-5} +z a^{-7} +2 z a^{-9} -z a^{-11} + a^{-2} +4 a^{-4} + a^{-6} - a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
