K12a1007

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1007

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^5-3 q^4+6 q^3-11 q^2+16 q-19+22 q^{-1} -21 q^{-2} +18 q^{-3} -13 q^{-4} +8 q^{-5} -4 q^{-6} + q^{-7} }
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^4+9 t^3-19 t^2+27 t-29+27 t^{-1} -19 t^{-2} +9 t^{-3} -2 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 -2 z^8-7 z^6-5 z^4+1}
Determinant	143
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 -a^2 z^8-z^8+a^4 z^6-4 a^2 z^6+z^6 a^{-2} -5 z^6+3 a^4 z^4-3 a^2 z^4+4 z^4 a^{-2} -9 z^4+a^4 z^2+3 a^2 z^2+4 z^2 a^{-2} -8 z^2-a^4+3 a^2+ a^{-2} -2}
Kauffman polynomial	$2az^{11}+2z^{11}a^{-1}+6a^{2}z^{10}+4z^{10}a^{-2}+10z^{10}+10a^{3}z^{9}+6az^{9}-z^{9}a^{-1}+3z^{9}a^{-3}+12a^{4}z^{8}-7a^{2}z^{8}-18z^{8}a^{-2}+z^{8}a^{-4}-38z^{8}+11a^{5}z^{7}-17a^{3}z^{7}-34az^{7}-21z^{7}a^{-1}-15z^{7}a^{-3}+8a^{6}z^{6}-19a^{4}z^{6}-11a^{2}z^{6}+26z^{6}a^{-2}-5z^{6}a^{-4}+47z^{6}+4a^{7}z^{5}-13a^{5}z^{5}+2a^{3}z^{5}+34az^{5}+39z^{5}a^{-1}+24z^{5}a^{-3}+a^{8}z^{4}-7a^{6}z^{4}+7a^{4}z^{4}+8a^{2}z^{4}-16z^{4}a^{-2}+7z^{4}a^{-4}-30z^{4}-2a^{7}z^{3}+3a^{5}z^{3}+4a^{3}z^{3}-11az^{3}-24z^{3}a^{-1}-14z^{3}a^{-3}+a^{6}z^{2}+5a^{2}z^{2}+5z^{2}a^{-2}-2z^{2}a^{-4}+13z^{2}+2az+4za^{-1}+2za^{-3}-a^{4}-3a^{2}-a^{-2}-2$

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