K12n181

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12n181

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^6+4 q^5-8 q^4+11 q^3-13 q^2+14 q-12+10 q^{-1} -6 q^{-2} +3 q^{-3} - q^{-4} }
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^3-9 t^2+19 t-23+19 t^{-1} -9 t^{-2} +2 t^{-3} }
Conway polynomial	$2z^{6}+3z^{4}+z^{2}+1$
Determinant	83
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^6 a^{-2} +z^6-a^2 z^4+2 z^4 a^{-2} -z^4 a^{-4} +3 z^4-2 a^2 z^2-z^2 a^{-4} +4 z^2-a^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 z^{10} a^{-2} +z^{10}+3 a z^9+6 z^9 a^{-1} +3 z^9 a^{-3} +3 a^2 z^8+6 z^8 a^{-2} +3 z^8 a^{-4} +6 z^8+a^3 z^7-7 a z^7-12 z^7 a^{-1} -3 z^7 a^{-3} +z^7 a^{-5} -12 a^2 z^6-21 z^6 a^{-2} -3 z^6 a^{-4} -30 z^6-4 a^3 z^5-4 a z^5-6 z^5 a^{-1} -2 z^5 a^{-3} +4 z^5 a^{-5} +15 a^2 z^4+16 z^4 a^{-2} +3 z^4 a^{-4} +4 z^4 a^{-6} +32 z^4+5 a^3 z^3+13 a z^3+14 z^3 a^{-1} +3 z^3 a^{-3} -2 z^3 a^{-5} +z^3 a^{-7} -7 a^2 z^2-6 z^2 a^{-2} -z^2 a^{-4} -z^2 a^{-6} -13 z^2-2 a^3 z-5 a z-5 z a^{-1} -2 z a^{-3} +a^2+ a^{-2} +3}

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