K12a108

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a108

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+9 q^7-18 q^6+27 q^5-34 q^4+38 q^3-35 q^2+30 q-21+12 q^{-1} -5 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 -t^4+8 t^3-26 t^2+51 t-63+51 t^{-1} -26 t^{-2} +8 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+2 z^4+3 z^2+1}
Determinant	235
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^8 a^{-2} -4 z^6 a^{-2} +3 z^6 a^{-4} +z^6-7 z^4 a^{-2} +10 z^4 a^{-4} -3 z^4 a^{-6} +2 z^4-5 z^2 a^{-2} +13 z^2 a^{-4} -7 z^2 a^{-6} +z^2 a^{-8} +z^2- a^{-2} +6 a^{-4} -5 a^{-6} + a^{-8} }
Kauffman polynomial	$2z^{11}a^{-3}+2z^{11}a^{-5}+8z^{10}a^{-2}+14z^{10}a^{-4}+6z^{10}a^{-6}+13z^{9}a^{-1}+24z^{9}a^{-3}+19z^{9}a^{-5}+8z^{9}a^{-7}+6z^{8}a^{-2}-6z^{8}a^{-4}+6z^{8}a^{-6}+7z^{8}a^{-8}+11z^{8}+5az^{7}-20z^{7}a^{-1}-55z^{7}a^{-3}-40z^{7}a^{-5}-6z^{7}a^{-7}+4z^{7}a^{-9}+a^{2}z^{6}-42z^{6}a^{-2}-39z^{6}a^{-4}-32z^{6}a^{-6}-12z^{6}a^{-8}+z^{6}a^{-10}-21z^{6}-8az^{5}+3z^{5}a^{-1}+31z^{5}a^{-3}+16z^{5}a^{-5}-13z^{5}a^{-7}-9z^{5}a^{-9}-a^{2}z^{4}+38z^{4}a^{-2}+52z^{4}a^{-4}+35z^{4}a^{-6}+6z^{4}a^{-8}-2z^{4}a^{-10}+12z^{4}+3az^{3}+3z^{3}a^{-1}+2z^{3}a^{-3}+15z^{3}a^{-5}+20z^{3}a^{-7}+7z^{3}a^{-9}-13z^{2}a^{-2}-25z^{2}a^{-4}-18z^{2}a^{-6}-2z^{2}a^{-8}+z^{2}a^{-10}-3z^{2}-za^{-1}-4za^{-3}-10za^{-5}-9za^{-7}-2za^{-9}+a^{-2}+6a^{-4}+5a^{-6}+a^{-8}$

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