K12a1120

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1120

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^3-6 q^2+9 q-12+16 q^{-1} -16 q^{-2} +16 q^{-3} -13 q^{-4} +9 q^{-5} -6 q^{-6} +3 q^{-7} - q^{-8} }
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^5-4 t^4+9 t^3-14 t^2+18 t-19+18 t^{-1} -14 t^{-2} +9 t^{-3} -4 t^{-4} + t^{-5} }
Conway polynomial	$z^{10}+6z^{8}+12z^{6}+10z^{4}+4z^{2}+1$
Determinant	111
Signature	-2
HOMFLY-PT polynomial	$a^{2}z^{10}-a^{4}z^{8}+8a^{2}z^{8}-z^{8}-6a^{4}z^{6}+24a^{2}z^{6}-6z^{6}-12a^{4}z^{4}+34a^{2}z^{4}-12z^{4}-10a^{4}z^{2}+24a^{2}z^{2}-10z^{2}-4a^{4}+8a^{2}-3$
Kauffman polynomial	$2a^{3}z^{11}+2az^{11}+4a^{4}z^{10}+9a^{2}z^{10}+5z^{10}+4a^{5}z^{9}-3a^{3}z^{9}-2az^{9}+5z^{9}a^{-1}+4a^{6}z^{8}-14a^{4}z^{8}-44a^{2}z^{8}+3z^{8}a^{-2}-23z^{8}+4a^{7}z^{7}-8a^{5}z^{7}-8a^{3}z^{7}-19az^{7}-22z^{7}a^{-1}+z^{7}a^{-3}+3a^{8}z^{6}-5a^{6}z^{6}+26a^{4}z^{6}+83a^{2}z^{6}-12z^{6}a^{-2}+37z^{6}+a^{9}z^{5}-6a^{7}z^{5}+8a^{5}z^{5}+27a^{3}z^{5}+44az^{5}+28z^{5}a^{-1}-4z^{5}a^{-3}-6a^{8}z^{4}-24a^{4}z^{4}-73a^{2}z^{4}+10z^{4}a^{-2}-33z^{4}-2a^{9}z^{3}-4a^{5}z^{3}-22a^{3}z^{3}-35az^{3}-16z^{3}a^{-1}+3z^{3}a^{-3}+2a^{8}z^{2}+15a^{4}z^{2}+33a^{2}z^{2}-z^{2}a^{-2}+15z^{2}+a^{9}z+2a^{5}z+8a^{3}z+9az+4za^{-1}-4a^{4}-8a^{2}-3$

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