K12a354
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^{10}+6 q^9-14 q^8+23 q^7-33 q^6+39 q^5-41 q^4+38 q^3-29 q^2+20 q-10+4 q^{-1} - q^{-2} }[/math] |
| Alexander polynomial | [math]\displaystyle{ 5 t^3-26 t^2+60 t-77+60 t^{-1} -26 t^{-2} +5 t^{-3} }[/math] |
| Conway polynomial | [math]\displaystyle{ 5 z^6+4 z^4+z^2+1 }[/math] |
| Determinant | 259 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ z^6 a^{-2} +3 z^6 a^{-4} +z^6 a^{-6} +8 z^4 a^{-4} -2 z^4 a^{-6} -z^4 a^{-8} -z^4-z^2 a^{-2} +10 z^2 a^{-4} -8 z^2 a^{-6} +z^2 a^{-8} -z^2+5 a^{-4} -6 a^{-6} +2 a^{-8} }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 4 z^{11} a^{-5} +4 z^{11} a^{-7} +12 z^{10} a^{-4} +24 z^{10} a^{-6} +12 z^{10} a^{-8} +17 z^9 a^{-3} +26 z^9 a^{-5} +22 z^9 a^{-7} +13 z^9 a^{-9} +15 z^8 a^{-2} -3 z^8 a^{-4} -45 z^8 a^{-6} -21 z^8 a^{-8} +6 z^8 a^{-10} +9 z^7 a^{-1} -27 z^7 a^{-3} -84 z^7 a^{-5} -84 z^7 a^{-7} -35 z^7 a^{-9} +z^7 a^{-11} -24 z^6 a^{-2} -37 z^6 a^{-4} -3 z^6 a^{-6} -7 z^6 a^{-8} -13 z^6 a^{-10} +4 z^6+a z^5-10 z^5 a^{-1} +19 z^5 a^{-3} +75 z^5 a^{-5} +70 z^5 a^{-7} +24 z^5 a^{-9} -z^5 a^{-11} +21 z^4 a^{-2} +51 z^4 a^{-4} +37 z^4 a^{-6} +16 z^4 a^{-8} +5 z^4 a^{-10} -4 z^4-a z^3+4 z^3 a^{-1} -6 z^3 a^{-3} -23 z^3 a^{-5} -12 z^3 a^{-7} -8 z^2 a^{-2} -26 z^2 a^{-4} -23 z^2 a^{-6} -4 z^2 a^{-8} +2 z^2 a^{-10} +z^2+2 z a^{-3} -5 z a^{-7} -3 z a^{-9} +5 a^{-4} +6 a^{-6} +2 a^{-8} }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
