K12a45

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a45

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^4+3 q^3-8 q^2+15 q-21+27 q^{-1} -28 q^{-2} +27 q^{-3} -22 q^{-4} +15 q^{-5} -8 q^{-6} +3 q^{-7} - q^{-8} }
Alexander polynomial	$-t^{4}+8t^{3}-22t^{2}+37t-43+37t^{-1}-22t^{-2}+8t^{-3}-t^{-4}$
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+6 z^4+5 z^2+1}
Determinant	179
Signature	-2
HOMFLY-PT polynomial	$-a^{2}z^{8}+2a^{4}z^{6}-4a^{2}z^{6}+2z^{6}-a^{6}z^{4}+7a^{4}z^{4}-6a^{2}z^{4}-z^{4}a^{-2}+7z^{4}-3a^{6}z^{2}+8a^{4}z^{2}-5a^{2}z^{2}-3z^{2}a^{-2}+8z^{2}-2a^{6}+3a^{4}-2a^{2}-2a^{-2}+4$
Kauffman polynomial	$a^{3}z^{11}+az^{11}+5a^{4}z^{10}+9a^{2}z^{10}+4z^{10}+9a^{5}z^{9}+19a^{3}z^{9}+15az^{9}+5z^{9}a^{-1}+9a^{6}z^{8}+7a^{4}z^{8}-7a^{2}z^{8}+3z^{8}a^{-2}-2z^{8}+6a^{7}z^{7}-12a^{5}z^{7}-55a^{3}z^{7}-52az^{7}-14z^{7}a^{-1}+z^{7}a^{-3}+3a^{8}z^{6}-15a^{6}z^{6}-37a^{4}z^{6}-29a^{2}z^{6}-10z^{6}a^{-2}-20z^{6}+a^{9}z^{5}-8a^{7}z^{5}+6a^{5}z^{5}+58a^{3}z^{5}+58az^{5}+11z^{5}a^{-1}-4z^{5}a^{-3}-4a^{8}z^{4}+16a^{6}z^{4}+45a^{4}z^{4}+42a^{2}z^{4}+11z^{4}a^{-2}+28z^{4}-2a^{9}z^{3}+5a^{7}z^{3}+2a^{5}z^{3}-30a^{3}z^{3}-33az^{3}-3z^{3}a^{-1}+5z^{3}a^{-3}+a^{8}z^{2}-9a^{6}z^{2}-20a^{4}z^{2}-20a^{2}z^{2}-6z^{2}a^{-2}-16z^{2}+a^{9}z-2a^{7}z-a^{5}z+7a^{3}z+7az-2za^{-3}+2a^{6}+3a^{4}+2a^{2}+2a^{-2}+4$

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