K12a9

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a9

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^7-3 q^6+6 q^5-10 q^4+14 q^3-17 q^2+18 q-16+14 q^{-1} -10 q^{-2} +6 q^{-3} -3 q^{-4} + q^{-5} }
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^3-12 t^2+28 t-35+28 t^{-1} -12 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^6-2 z^2+1}
Determinant	119
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^6-2 a^2 z^4+2 z^4 a^{-2} -2 z^4 a^{-4} +2 z^4+a^4 z^2-4 a^2 z^2+2 z^2 a^{-2} -4 z^2 a^{-4} +z^2 a^{-6} +2 z^2+a^4-2 a^2+ a^{-2} -2 a^{-4} + a^{-6} +2}
Kauffman polynomial	$az^{11}+z^{11}a^{-1}+3a^{2}z^{10}+4z^{10}a^{-2}+7z^{10}+3a^{3}z^{9}+6az^{9}+9z^{9}a^{-1}+6z^{9}a^{-3}+a^{4}z^{8}-10a^{2}z^{8}-5z^{8}a^{-2}+6z^{8}a^{-4}-22z^{8}-15a^{3}z^{7}-42az^{7}-43z^{7}a^{-1}-10z^{7}a^{-3}+6z^{7}a^{-5}-5a^{4}z^{6}+a^{2}z^{6}-6z^{6}a^{-2}-4z^{6}a^{-4}+5z^{6}a^{-6}+9z^{6}+24a^{3}z^{5}+66az^{5}+54z^{5}a^{-1}+4z^{5}a^{-3}-5z^{5}a^{-5}+3z^{5}a^{-7}+8a^{4}z^{4}+17a^{2}z^{4}+3z^{4}a^{-2}-8z^{4}a^{-4}-5z^{4}a^{-6}+z^{4}a^{-8}+14z^{4}-15a^{3}z^{3}-37az^{3}-29z^{3}a^{-1}-4z^{3}a^{-3}-3z^{3}a^{-7}-5a^{4}z^{2}-12a^{2}z^{2}+2z^{2}a^{-2}+8z^{2}a^{-4}+3z^{2}a^{-6}-z^{2}a^{-8}-9z^{2}+3a^{3}z+7az+6za^{-1}+2za^{-3}+za^{-5}+za^{-7}+a^{4}+2a^{2}-a^{-2}-2a^{-4}-a^{-6}+2$

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