K12a1011

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1011

Polynomial invariants

Jones polynomial	$q^{6}-3q^{5}+6q^{4}-10q^{3}+14q^{2}-17q+19-17q^{-1}+14q^{-2}-10q^{-3}+6q^{-4}-3q^{-5}+q^{-6}$
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^5+4 t^4-9 t^3+15 t^2-20 t+23-20 t^{-1} +15 t^{-2} -9 t^{-3} +4 t^{-4} - t^{-5} }
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^{10}-6 z^8-12 z^6-9 z^4-2 z^2+1}
Determinant	121
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^{10}+a^2 z^8+z^8 a^{-2} -8 z^8+6 a^2 z^6+6 z^6 a^{-2} -24 z^6+12 a^2 z^4+12 z^4 a^{-2} -33 z^4+9 a^2 z^2+9 z^2 a^{-2} -20 z^2+2 a^2+2 a^{-2} -3}
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 2 a z^{11}+2 z^{11} a^{-1} +4 a^2 z^{10}+5 z^{10} a^{-2} +9 z^{10}+4 a^3 z^9-3 a z^9-z^9 a^{-1} +6 z^9 a^{-3} +4 a^4 z^8-14 a^2 z^8-19 z^8 a^{-2} +5 z^8 a^{-4} -42 z^8+3 a^5 z^7-9 a^3 z^7-5 a z^7-18 z^7 a^{-1} -22 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-10 a^4 z^6+26 a^2 z^6+29 z^6 a^{-2} -16 z^6 a^{-4} +z^6 a^{-6} +83 z^6-9 a^5 z^5+4 a^3 z^5+22 a z^5+46 z^5 a^{-1} +28 z^5 a^{-3} -9 z^5 a^{-5} -3 a^6 z^4+4 a^4 z^4-27 a^2 z^4-20 z^4 a^{-2} +12 z^4 a^{-4} -3 z^4 a^{-6} -69 z^4+6 a^5 z^3-a^3 z^3-18 a z^3-31 z^3 a^{-1} -16 z^3 a^{-3} +4 z^3 a^{-5} +2 a^6 z^2+12 a^2 z^2+9 z^2 a^{-2} -3 z^2 a^{-4} +z^2 a^{-6} +27 z^2-a^5 z+4 a z+6 z a^{-1} +3 z a^{-3} -2 a^2-2 a^{-2} -3}

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