K12a104

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a104

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+3 q-7+13 q^{-1} -18 q^{-2} +24 q^{-3} -25 q^{-4} +24 q^{-5} -20 q^{-6} +14 q^{-7} -9 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^3-17 t^2+37 t-47+37 t^{-1} -17 t^{-2} +4 t^{-3} }
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 4 z^6+7 z^4+5 z^2+1}
Determinant	163
Signature	-2
HOMFLY-PT polynomial	$-z^{4}a^{8}-z^{2}a^{8}+z^{6}a^{6}+z^{4}a^{6}-2z^{2}a^{6}-3a^{6}+2z^{6}a^{4}+6z^{4}a^{4}+8z^{2}a^{4}+4a^{4}+z^{6}a^{2}+2z^{4}a^{2}+2z^{2}a^{2}+a^{2}-z^{4}-2z^{2}-1$
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}+3 z^3 a^{11}-z a^{11}+4 z^8 a^{10}-13 z^6 a^{10}+12 z^4 a^{10}-3 z^2 a^{10}+6 z^9 a^9-17 z^7 a^9+10 z^5 a^9+2 z^3 a^9-z a^9+4 z^{10} a^8-2 z^8 a^8-20 z^6 a^8+21 z^4 a^8-4 z^2 a^8+z^{11} a^7+11 z^9 a^7-32 z^7 a^7+15 z^5 a^7+8 z^3 a^7-6 z a^7+7 z^{10} a^6-4 z^8 a^6-23 z^6 a^6+26 z^4 a^6-11 z^2 a^6+3 a^6+z^{11} a^5+10 z^9 a^5-17 z^7 a^5-6 z^5 a^5+21 z^3 a^5-10 z a^5+3 z^{10} a^4+8 z^8 a^4-24 z^6 a^4+22 z^4 a^4-11 z^2 a^4+4 a^4+5 z^9 a^3+2 z^7 a^3-15 z^5 a^3+16 z^3 a^3-5 z a^3+6 z^8 a^2-5 z^6 a^2+2 z^2 a^2-a^2+5 z^7 a-6 z^5 a+2 z^3 a+3 z^6-5 z^4+3 z^2-1+z^5 a^{-1} -2 z^3 a^{-1} +z a^{-1} }

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