K12a1110

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1110

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^{10}+5 q^9-13 q^8+23 q^7-34 q^6+42 q^5-45 q^4+43 q^3-34 q^2+24 q-13+5 q^{-1} - q^{-2} }
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 5 t^3-27 t^2+66 t-87+66 t^{-1} -27 t^{-2} +5 t^{-3} }
Conway polynomial	$5z^{6}+3z^{4}+3z^{2}+1$
Determinant	283
Signature	2
HOMFLY-PT polynomial	$z^{6}a^{-2}+3z^{6}a^{-4}+z^{6}a^{-6}-z^{4}a^{-2}+7z^{4}a^{-4}-z^{4}a^{-6}-z^{4}a^{-8}-z^{4}-2z^{2}a^{-2}+8z^{2}a^{-4}-3z^{2}a^{-6}+3a^{-4}-2a^{-6}$
Kauffman 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 5 z^{11} a^{-5} +5 z^{11} a^{-7} +16 z^{10} a^{-4} +28 z^{10} a^{-6} +12 z^{10} a^{-8} +24 z^9 a^{-3} +30 z^9 a^{-5} +17 z^9 a^{-7} +11 z^9 a^{-9} +22 z^8 a^{-2} -5 z^8 a^{-4} -56 z^8 a^{-6} -24 z^8 a^{-8} +5 z^8 a^{-10} +13 z^7 a^{-1} -35 z^7 a^{-3} -89 z^7 a^{-5} -71 z^7 a^{-7} -29 z^7 a^{-9} +z^7 a^{-11} -32 z^6 a^{-2} -41 z^6 a^{-4} +15 z^6 a^{-6} +7 z^6 a^{-8} -12 z^6 a^{-10} +5 z^6+a z^5-12 z^5 a^{-1} +11 z^5 a^{-3} +60 z^5 a^{-5} +62 z^5 a^{-7} +24 z^5 a^{-9} -2 z^5 a^{-11} +18 z^4 a^{-2} +41 z^4 a^{-4} +17 z^4 a^{-6} +4 z^4 a^{-8} +8 z^4 a^{-10} -2 z^4+3 z^3 a^{-1} +5 z^3 a^{-3} -3 z^3 a^{-5} -14 z^3 a^{-7} -8 z^3 a^{-9} +z^3 a^{-11} -5 z^2 a^{-2} -14 z^2 a^{-4} -9 z^2 a^{-6} -z^2 a^{-8} -z^2 a^{-10} -z a^{-1} -3 z a^{-3} -5 z a^{-5} -2 z a^{-7} +z a^{-9} +3 a^{-4} +2 a^{-6} }

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