K12a1
From Knot Atlas
Jump to navigationJump to search
Polynomial invariants
| Jones polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -q^5+4 q^4-10 q^3+19 q^2-26 q+32-34 q^{-1} +31 q^{-2} -25 q^{-3} +17 q^{-4} -9 q^{-5} +4 q^{-6} - q^{-7} } |
| Alexander polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle t^4-7 t^3+23 t^2-46 t+59-46 t^{-1} +23 t^{-2} -7 t^{-3} + t^{-4} } |
| Conway polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^8+z^6+z^4-z^2+1} |
| Determinant | 213 |
| Signature | 0 |
| HOMFLY-PT polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z^8-3 a^2 z^6-z^6 a^{-2} +5 z^6+3 a^4 z^4-11 a^2 z^4-3 z^4 a^{-2} +12 z^4-a^6 z^2+7 a^4 z^2-16 a^2 z^2-4 z^2 a^{-2} +13 z^2-a^6+5 a^4-8 a^2- a^{-2} +6} |
| Kauffman polynomial | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^3 z^{11}+a z^{11}+4 a^4 z^{10}+10 a^2 z^{10}+6 z^{10}+6 a^5 z^9+20 a^3 z^9+27 a z^9+13 z^9 a^{-1} +4 a^6 z^8+7 a^4 z^8+8 a^2 z^8+14 z^8 a^{-2} +19 z^8+a^7 z^7-14 a^5 z^7-56 a^3 z^7-64 a z^7-14 z^7 a^{-1} +9 z^7 a^{-3} -13 a^6 z^6-49 a^4 z^6-81 a^2 z^6-23 z^6 a^{-2} +4 z^6 a^{-4} -72 z^6-3 a^7 z^5+6 a^5 z^5+41 a^3 z^5+44 a z^5-11 z^5 a^{-3} +z^5 a^{-5} +15 a^6 z^4+62 a^4 z^4+101 a^2 z^4+21 z^4 a^{-2} -4 z^4 a^{-4} +79 z^4+3 a^7 z^3+4 a^5 z^3-9 a^3 z^3-12 a z^3+5 z^3 a^{-1} +6 z^3 a^{-3} -z^3 a^{-5} -7 a^6 z^2-30 a^4 z^2-50 a^2 z^2-10 z^2 a^{-2} +z^2 a^{-4} -38 z^2-a^7 z-2 a^5 z+a^3 z+2 a z-z a^{-1} -z a^{-3} +a^6+5 a^4+8 a^2+ a^{-2} +6} |
Modifying This Page
| Read me first: Modifying Knot Pages
See/edit the Large Knot Page master template. Back to the top. |
