K12a801
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ q^{13}-4 q^{12}+9 q^{11}-14 q^{10}+19 q^9-21 q^8+20 q^7-19 q^6+13 q^5-8 q^4+5 q^3-q^2+q }[/math] |
| Alexander polynomial | [math]\displaystyle{ -2 t^4+8 t^3-17 t^2+26 t-29+26 t^{-1} -17 t^{-2} +8 t^{-3} -2 t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -2 z^8-8 z^6-9 z^4-2 z^2+1 }[/math] |
| Determinant | 135 |
| Signature | 6 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-6} -z^8 a^{-8} +z^6 a^{-4} -6 z^6 a^{-6} -4 z^6 a^{-8} +z^6 a^{-10} +6 z^4 a^{-4} -15 z^4 a^{-6} -3 z^4 a^{-8} +3 z^4 a^{-10} +12 z^2 a^{-4} -20 z^2 a^{-6} +4 z^2 a^{-8} +2 z^2 a^{-10} +8 a^{-4} -12 a^{-6} +5 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ z^{11} a^{-7} +z^{11} a^{-9} +z^{10} a^{-6} +5 z^{10} a^{-8} +4 z^{10} a^{-10} +z^9 a^{-5} -2 z^9 a^{-7} +6 z^9 a^{-9} +9 z^9 a^{-11} +z^8 a^{-4} -13 z^8 a^{-8} +z^8 a^{-10} +13 z^8 a^{-12} -3 z^7 a^{-5} +8 z^7 a^{-7} -13 z^7 a^{-9} -11 z^7 a^{-11} +13 z^7 a^{-13} -7 z^6 a^{-4} -15 z^6 a^{-6} +10 z^6 a^{-8} -10 z^6 a^{-10} -19 z^6 a^{-12} +9 z^6 a^{-14} -3 z^5 a^{-5} -37 z^5 a^{-7} -13 z^5 a^{-9} -17 z^5 a^{-13} +4 z^5 a^{-15} +18 z^4 a^{-4} +34 z^4 a^{-6} -9 z^4 a^{-8} -10 z^4 a^{-10} +6 z^4 a^{-12} -8 z^4 a^{-14} +z^4 a^{-16} +16 z^3 a^{-5} +56 z^3 a^{-7} +29 z^3 a^{-9} -3 z^3 a^{-11} +7 z^3 a^{-13} -z^3 a^{-15} -20 z^2 a^{-4} -30 z^2 a^{-6} +4 z^2 a^{-8} +11 z^2 a^{-10} +3 z^2 a^{-14} -12 z a^{-5} -26 z a^{-7} -14 z a^{-9} +8 a^{-4} +12 a^{-6} +5 a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
