K12a1003

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1003

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+4-10 q^{-1} +19 q^{-2} -27 q^{-3} +35 q^{-4} -37 q^{-5} +35 q^{-6} -29 q^{-7} +20 q^{-8} -11 q^{-9} +4 q^{-10} - q^{-11} }
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 2 t^4-10 t^3+28 t^2-48 t+57-48 t^{-1} +28 t^{-2} -10 t^{-3} +2 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 2 z^8+6 z^6+8 z^4+6 z^2+1}
Determinant	233
Signature	-4
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^6 a^8-3 z^4 a^8-4 z^2 a^8-2 a^8+z^8 a^6+4 z^6 a^6+7 z^4 a^6+6 z^2 a^6+a^6+z^8 a^4+4 z^6 a^4+7 z^4 a^4+7 z^2 a^4+3 a^4-z^6 a^2-3 z^4 a^2-3 z^2 a^2-a^2}
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^5 a^{13}-z^3 a^{13}+4 z^6 a^{12}-3 z^4 a^{12}+10 z^7 a^{11}-13 z^5 a^{11}+9 z^3 a^{11}-3 z a^{11}+16 z^8 a^{10}-26 z^6 a^{10}+20 z^4 a^{10}-6 z^2 a^{10}+17 z^9 a^9-27 z^7 a^9+16 z^5 a^9-3 z^3 a^9+z a^9+11 z^{10} a^8-5 z^8 a^8-19 z^6 a^8+16 z^4 a^8-2 a^8+3 z^{11} a^7+23 z^9 a^7-69 z^7 a^7+65 z^5 a^7-31 z^3 a^7+6 z a^7+18 z^{10} a^6-34 z^8 a^6+10 z^6 a^6+3 z^4 a^6-a^6+3 z^{11} a^5+13 z^9 a^5-50 z^7 a^5+47 z^5 a^5-19 z^3 a^5+2 z a^5+7 z^{10} a^4-9 z^8 a^4-13 z^6 a^4+22 z^4 a^4-11 z^2 a^4+3 a^4+7 z^9 a^3-17 z^7 a^3+9 z^5 a^3+2 z^3 a^3-z a^3+4 z^8 a^2-12 z^6 a^2+12 z^4 a^2-5 z^2 a^2+a^2+z^7 a-3 z^5 a+3 z^3 a-z a}

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