K12a1103

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1103

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^2+4 q-9+16 q^{-1} -23 q^{-2} +29 q^{-3} -30 q^{-4} +29 q^{-5} -23 q^{-6} +16 q^{-7} -10 q^{-8} +4 q^{-9} - q^{-10} }
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 4 t^3-19 t^2+45 t-59+45 t^{-1} -19 t^{-2} +4 t^{-3} }
Conway polynomial	$4z^{6}+5z^{4}+5z^{2}+1$
Determinant	195
Signature	-2
HOMFLY-PT polynomial	$-z^{4}a^{8}-z^{2}a^{8}-a^{8}+z^{6}a^{6}+z^{4}a^{6}-a^{6}+2z^{6}a^{4}+5z^{4}a^{4}+7z^{2}a^{4}+4a^{4}+z^{6}a^{2}+z^{4}a^{2}-a^{2}-z^{4}-z^{2}$
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 z^7 a^{11}-3 z^5 a^{11}+2 z^3 a^{11}+4 z^8 a^{10}-12 z^6 a^{10}+8 z^4 a^{10}-z^2 a^{10}+8 z^9 a^9-27 z^7 a^9+29 z^5 a^9-18 z^3 a^9+7 z a^9+8 z^{10} a^8-23 z^8 a^8+19 z^6 a^8-9 z^4 a^8+3 z^2 a^8-a^8+3 z^{11} a^7+8 z^9 a^7-51 z^7 a^7+71 z^5 a^7-43 z^3 a^7+10 z a^7+16 z^{10} a^6-45 z^8 a^6+39 z^6 a^6-5 z^4 a^6-7 z^2 a^6+a^6+3 z^{11} a^5+11 z^9 a^5-47 z^7 a^5+56 z^5 a^5-24 z^3 a^5+3 z a^5+8 z^{10} a^4-7 z^8 a^4-13 z^6 a^4+27 z^4 a^4-16 z^2 a^4+4 a^4+11 z^9 a^3-16 z^7 a^3+5 z^5 a^3+4 z^3 a^3-z a^3+11 z^8 a^2-17 z^6 a^2+10 z^4 a^2-4 z^2 a^2+a^2+8 z^7 a-11 z^5 a+4 z^3 a-z a+4 z^6-5 z^4+z^2+z^5 a^{-1} -z^3 a^{-1} }

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