K12a1043

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1043

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^8+4 q^7-9 q^6+16 q^5-24 q^4+30 q^3-32 q^2+31 q-25+18 q^{-1} -11 q^{-2} +5 q^{-3} - q^{-4} }
Alexander polynomial	$4t^{3}-21t^{2}+48t-61+48t^{-1}-21t^{-2}+4t^{-3}$
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 4 z^6+3 z^4+1}
Determinant	207
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 2 z^6 a^{-2} +z^6 a^{-4} +z^6-a^2 z^4+4 z^4 a^{-2} +z^4 a^{-4} -z^4 a^{-6} +4 z^2 a^{-2} -z^2 a^{-6} -3 z^2+a^2+3 a^{-2} - a^{-4} -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 4 z^{11} a^{-1} +4 z^{11} a^{-3} +20 z^{10} a^{-2} +10 z^{10} a^{-4} +10 z^{10}+10 a z^9+6 z^9 a^{-1} +8 z^9 a^{-3} +12 z^9 a^{-5} +5 a^2 z^8-64 z^8 a^{-2} -19 z^8 a^{-4} +11 z^8 a^{-6} -29 z^8+a^3 z^7-32 a z^7-49 z^7 a^{-1} -45 z^7 a^{-3} -21 z^7 a^{-5} +8 z^7 a^{-7} -14 a^2 z^6+76 z^6 a^{-2} +19 z^6 a^{-4} -16 z^6 a^{-6} +4 z^6 a^{-8} +23 z^6-2 a^3 z^5+26 a z^5+58 z^5 a^{-1} +59 z^5 a^{-3} +17 z^5 a^{-5} -11 z^5 a^{-7} +z^5 a^{-9} +7 a^2 z^4-44 z^4 a^{-2} -13 z^4 a^{-4} +7 z^4 a^{-6} -5 z^4 a^{-8} -12 z^4-5 a z^3-21 z^3 a^{-1} -29 z^3 a^{-3} -8 z^3 a^{-5} +4 z^3 a^{-7} -z^3 a^{-9} +a^2 z^2+14 z^2 a^{-2} +5 z^2 a^{-4} +z^2 a^{-8} +9 z^2+2 z a^{-1} +4 z a^{-3} +2 z a^{-5} -a^2-3 a^{-2} - a^{-4} -2}

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