K12a1118

Knot presentations

Dowker-Thistlethwaite code

6 12 22 20 18 16 4 24 10 8 2 14

Notes on presentations of K12a1118

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^2+3 q-6+10 q^{-1} -13 q^{-2} +17 q^{-3} -17 q^{-4} +16 q^{-5} -13 q^{-6} +9 q^{-7} -6 q^{-8} +3 q^{-9} - q^{-10} }
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 3 t^3-12 t^2+26 t-33+26 t^{-1} -12 t^{-2} +3 t^{-3} }
Conway polynomial	$3z^{6}+6z^{4}+5z^{2}+1$
Determinant	115
Signature	-2
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^4 a^8-2 z^2 a^8-a^8+z^6 a^6+3 z^4 a^6+3 z^2 a^6+z^6 a^4+2 z^4 a^4+2 z^2 a^4+a^4+z^6 a^2+3 z^4 a^2+4 z^2 a^2+2 a^2-z^4-2 z^2-1}
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 z^7 a^{11}-4 z^5 a^{11}+3 z^3 a^{11}+3 z^8 a^{10}-12 z^6 a^{10}+10 z^4 a^{10}-z^2 a^{10}+5 z^9 a^9-22 z^7 a^9+29 z^5 a^9-19 z^3 a^9+6 z a^9+5 z^{10} a^8-22 z^8 a^8+32 z^6 a^8-24 z^4 a^8+8 z^2 a^8-a^8+2 z^{11} a^7-z^9 a^7-24 z^7 a^7+53 z^5 a^7-40 z^3 a^7+8 z a^7+9 z^{10} a^6-41 z^8 a^6+68 z^6 a^6-45 z^4 a^6+10 z^2 a^6+2 z^{11} a^5-2 z^9 a^5-11 z^7 a^5+28 z^5 a^5-16 z^3 a^5+2 z a^5+4 z^{10} a^4-12 z^8 a^4+18 z^6 a^4-11 z^4 a^4+4 z^2 a^4+a^4+4 z^9 a^3-6 z^7 a^3+2 z^5 a^3+2 z^3 a^3+4 z^8 a^2-3 z^6 a^2-6 z^4 a^2+6 z^2 a^2-2 a^2+4 z^7 a-5 z^5 a-2 z^3 a+z a+3 z^6-6 z^4+3 z^2-1+z^5 a^{-1} -2 z^3 a^{-1} +z a^{-1} }

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Large Knot Page master template. Back to the top.