K12a844
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | [math]\displaystyle{ -q^8+4 q^7-10 q^6+18 q^5-26 q^4+31 q^3-32 q^2+30 q-23+16 q^{-1} -8 q^{-2} +3 q^{-3} - q^{-4} }[/math] |
| Alexander polynomial | [math]\displaystyle{ -t^4+8 t^3-24 t^2+43 t-51+43 t^{-1} -24 t^{-2} +8 t^{-3} - t^{-4} }[/math] |
| Conway polynomial | [math]\displaystyle{ -z^8+4 z^4+3 z^2+1 }[/math] |
| Determinant | 203 |
| Signature | 2 |
| HOMFLY-PT polynomial | [math]\displaystyle{ -z^8 a^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-7 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +7 z^4-3 a^2 z^2-7 z^2 a^{-2} +6 z^2 a^{-4} -2 z^2 a^{-6} +9 z^2-2 a^2-3 a^{-2} +2 a^{-4} - a^{-6} +5 }[/math] |
| Kauffman polynomial | [math]\displaystyle{ 2 z^{11} a^{-1} +2 z^{11} a^{-3} +13 z^{10} a^{-2} +8 z^{10} a^{-4} +5 z^{10}+5 a z^9+11 z^9 a^{-1} +20 z^9 a^{-3} +14 z^9 a^{-5} +3 a^2 z^8-22 z^8 a^{-2} +2 z^8 a^{-4} +14 z^8 a^{-6} -7 z^8+a^3 z^7-13 a z^7-42 z^7 a^{-1} -60 z^7 a^{-3} -23 z^7 a^{-5} +9 z^7 a^{-7} -10 a^2 z^6-4 z^6 a^{-2} -35 z^6 a^{-4} -25 z^6 a^{-6} +4 z^6 a^{-8} -8 z^6-4 a^3 z^5+8 a z^5+44 z^5 a^{-1} +58 z^5 a^{-3} +13 z^5 a^{-5} -12 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4+23 z^4 a^{-2} +42 z^4 a^{-4} +21 z^4 a^{-6} -4 z^4 a^{-8} +17 z^4+5 a^3 z^3+a z^3-21 z^3 a^{-1} -23 z^3 a^{-3} +z^3 a^{-5} +6 z^3 a^{-7} -z^3 a^{-9} -6 a^2 z^2-16 z^2 a^{-2} -16 z^2 a^{-4} -8 z^2 a^{-6} -14 z^2-2 a^3 z-2 a z+2 z a^{-1} +3 z a^{-3} -z a^{-5} -2 z a^{-7} +2 a^2+3 a^{-2} +2 a^{-4} + a^{-6} +5 }[/math] |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
