K12a537

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a537

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^9-4 q^8+8 q^7-14 q^6+21 q^5-26 q^4+28 q^3-26 q^2+22 q-15+9 q^{-1} -4 q^{-2} + q^{-3} }
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^3-15 t^2+43 t-59+43 t^{-1} -15 t^{-2} +2 t^{-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 2 z^6-3 z^4+z^2+1}
Determinant	179
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^{-4} +z^4 a^{-4} -2 z^4 a^{-6} -2 z^4+a^2 z^2-z^2 a^{-2} +3 z^2 a^{-4} -2 z^2 a^{-6} +z^2 a^{-8} -z^2- a^{-2} +2 a^{-4} - a^{-6} +1}
Kauffman polynomial	$z^{11}a^{-3}+z^{11}a^{-5}+4z^{10}a^{-2}+8z^{10}a^{-4}+4z^{10}a^{-6}+7z^{9}a^{-1}+14z^{9}a^{-3}+14z^{9}a^{-5}+7z^{9}a^{-7}+5z^{8}a^{-2}-5z^{8}a^{-4}+4z^{8}a^{-6}+7z^{8}a^{-8}+7z^{8}+4az^{7}-10z^{7}a^{-1}-36z^{7}a^{-3}-39z^{7}a^{-5}-13z^{7}a^{-7}+4z^{7}a^{-9}+a^{2}z^{6}-25z^{6}a^{-2}-18z^{6}a^{-4}-28z^{6}a^{-6}-18z^{6}a^{-8}+z^{6}a^{-10}-15z^{6}-9az^{5}+z^{5}a^{-1}+38z^{5}a^{-3}+43z^{5}a^{-5}+5z^{5}a^{-7}-10z^{5}a^{-9}-2a^{2}z^{4}+24z^{4}a^{-2}+31z^{4}a^{-4}+34z^{4}a^{-6}+14z^{4}a^{-8}-2z^{4}a^{-10}+9z^{4}+5az^{3}-2z^{3}a^{-1}-22z^{3}a^{-3}-19z^{3}a^{-5}+z^{3}a^{-7}+5z^{3}a^{-9}+a^{2}z^{2}-11z^{2}a^{-2}-15z^{2}a^{-4}-12z^{2}a^{-6}-4z^{2}a^{-8}-3z^{2}+2za^{-1}+5za^{-3}+3za^{-5}+a^{-2}+2a^{-4}+a^{-6}+1$

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