K12a1000

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1000

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^4-7 q^3+12 q^2-18 q+23-23 q^{-1} +23 q^{-2} -18 q^{-3} +13 q^{-4} -8 q^{-5} +3 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^4-8 t^3+19 t^2-30 t+35-30 t^{-1} +19 t^{-2} -8 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+8 z^6+11 z^4+6 z^2+1}
Determinant	153
Signature	0
HOMFLY-PT polynomial	$a^{2}z^{8}+z^{8}-a^{4}z^{6}+5a^{2}z^{6}-z^{6}a^{-2}+5z^{6}-4a^{4}z^{4}+10a^{2}z^{4}-4z^{4}a^{-2}+9z^{4}-6a^{4}z^{2}+11a^{2}z^{2}-5z^{2}a^{-2}+6z^{2}-4a^{4}+6a^{2}-2a^{-2}+1$
Kauffman polynomial	$2a^{3}z^{11}+2az^{11}+5a^{4}z^{10}+11a^{2}z^{10}+6z^{10}+5a^{5}z^{9}+5a^{3}z^{9}+8az^{9}+8z^{9}a^{-1}+3a^{6}z^{8}-14a^{4}z^{8}-35a^{2}z^{8}+7z^{8}a^{-2}-11z^{8}+a^{7}z^{7}-16a^{5}z^{7}-36a^{3}z^{7}-43az^{7}-19z^{7}a^{-1}+5z^{7}a^{-3}-10a^{6}z^{6}+12a^{4}z^{6}+38a^{2}z^{6}-13z^{6}a^{-2}+3z^{6}a^{-4}-4a^{7}z^{5}+15a^{5}z^{5}+57a^{3}z^{5}+66az^{5}+20z^{5}a^{-1}-7z^{5}a^{-3}+z^{5}a^{-5}+8a^{6}z^{4}-13a^{4}z^{4}-17a^{2}z^{4}+11z^{4}a^{-2}-5z^{4}a^{-4}+20z^{4}+5a^{7}z^{3}-11a^{5}z^{3}-46a^{3}z^{3}-38az^{3}-5z^{3}a^{-1}+z^{3}a^{-3}-2z^{3}a^{-5}-a^{6}z^{2}+9a^{4}z^{2}+8a^{2}z^{2}-7z^{2}a^{-2}+z^{2}a^{-4}-10z^{2}-2a^{7}z+5a^{5}z+15a^{3}z+10az-za^{-3}+za^{-5}-4a^{4}-6a^{2}+2a^{-2}+1$

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