K12a1039

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1039

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^6-3 q^5+7 q^4-11 q^3+16 q^2-20 q+21-20 q^{-1} +16 q^{-2} -11 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }
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 t^4-7 t^3+17 t^2-27 t+33-27 t^{-1} +17 t^{-2} -7 t^{-3} + 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 z^8+z^6-5 z^4-6 z^2+1}
Determinant	137
Signature	0
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^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-8 a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} +9 z^4+3 a^4 z^2-9 a^2 z^2-9 z^2 a^{-2} +3 z^2 a^{-4} +6 z^2+2 a^4-2 a^2-2 a^{-2} +2 a^{-4} +1}
Kauffman polynomial	$az^{11}+z^{11}a^{-1}+3a^{2}z^{10}+3z^{10}a^{-2}+6z^{10}+5a^{3}z^{9}+6az^{9}+6z^{9}a^{-1}+5z^{9}a^{-3}+5a^{4}z^{8}-a^{2}z^{8}-z^{8}a^{-2}+5z^{8}a^{-4}-12z^{8}+3a^{5}z^{7}-12a^{3}z^{7}-20az^{7}-20z^{7}a^{-1}-12z^{7}a^{-3}+3z^{7}a^{-5}+a^{6}z^{6}-14a^{4}z^{6}-12a^{2}z^{6}-12z^{6}a^{-2}-14z^{6}a^{-4}+z^{6}a^{-6}+6z^{6}-8a^{5}z^{5}+11a^{3}z^{5}+21az^{5}+21z^{5}a^{-1}+11z^{5}a^{-3}-8z^{5}a^{-5}-3a^{6}z^{4}+13a^{4}z^{4}+20a^{2}z^{4}+20z^{4}a^{-2}+13z^{4}a^{-4}-3z^{4}a^{-6}+8z^{4}+4a^{5}z^{3}-8a^{3}z^{3}-az^{3}-z^{3}a^{-1}-8z^{3}a^{-3}+4z^{3}a^{-5}+2a^{6}z^{2}-9a^{4}z^{2}-12a^{2}z^{2}-12z^{2}a^{-2}-9z^{2}a^{-4}+2z^{2}a^{-6}-2z^{2}+a^{3}z-3az-3za^{-1}+za^{-3}+2a^{4}+2a^{2}+2a^{-2}+2a^{-4}+1$

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