K12a1069

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1069

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^9-4 q^8+10 q^7-19 q^6+28 q^5-35 q^4+38 q^3-35 q^2+29 q-20+11 q^{-1} -4 q^{-2} + q^{-3} }
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^3-19 t^2+57 t-79+57 t^{-1} -19 t^{-2} +2 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 2 z^6-7 z^4-z^2+1}
Determinant	235
Signature	2
HOMFLY-PT polynomial	$z^{6}a^{-2}+z^{6}a^{-4}-2z^{4}a^{-2}-z^{4}a^{-4}-2z^{4}a^{-6}-2z^{4}+a^{2}z^{2}-4z^{2}a^{-2}+z^{2}a^{-8}+z^{2}-2a^{-2}+a^{-4}+2$
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 3 z^{11} a^{-3} +3 z^{11} a^{-5} +9 z^{10} a^{-2} +18 z^{10} a^{-4} +9 z^{10} a^{-6} +12 z^9 a^{-1} +19 z^9 a^{-3} +18 z^9 a^{-5} +11 z^9 a^{-7} -5 z^8 a^{-2} -32 z^8 a^{-4} -10 z^8 a^{-6} +8 z^8 a^{-8} +9 z^8+4 a z^7-23 z^7 a^{-1} -59 z^7 a^{-3} -58 z^7 a^{-5} -22 z^7 a^{-7} +4 z^7 a^{-9} +a^2 z^6-19 z^6 a^{-2} +15 z^6 a^{-4} -z^6 a^{-6} -15 z^6 a^{-8} +z^6 a^{-10} -18 z^6-7 a z^5+18 z^5 a^{-1} +65 z^5 a^{-3} +68 z^5 a^{-5} +20 z^5 a^{-7} -8 z^5 a^{-9} -2 a^2 z^4+26 z^4 a^{-2} +4 z^4 a^{-4} +4 z^4 a^{-6} +8 z^4 a^{-8} -2 z^4 a^{-10} +14 z^4+3 a z^3-12 z^3 a^{-1} -35 z^3 a^{-3} -37 z^3 a^{-5} -13 z^3 a^{-7} +4 z^3 a^{-9} +a^2 z^2-14 z^2 a^{-2} -3 z^2 a^{-4} -z^2 a^{-6} -2 z^2 a^{-8} +z^2 a^{-10} -8 z^2+3 z a^{-1} +8 z a^{-3} +8 z a^{-5} +3 z a^{-7} +2 a^{-2} + a^{-4} +2}

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