K12a1106

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1106

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^8-4 q^7+10 q^6-17 q^5+24 q^4-30 q^3+32 q^2-30 q+25-17 q^{-1} +10 q^{-2} -4 q^{-3} + q^{-4} }
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 -3 t^3+18 t^2-48 t+67-48 t^{-1} +18 t^{-2} -3 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 -3 z^6-3 z^2+1}
Determinant	205
Signature	0
HOMFLY-PT polynomial	$-2z^{6}a^{-2}-z^{6}+a^{2}z^{4}-5z^{4}a^{-2}+5z^{4}a^{-4}-z^{4}+a^{2}z^{2}-8z^{2}a^{-2}+9z^{2}a^{-4}-4z^{2}a^{-6}-z^{2}+a^{2}-4a^{-2}+5a^{-4}-3a^{-6}+a^{-8}+1$
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 3 z^{11} a^{-3} +3 z^{11} a^{-5} +12 z^{10} a^{-2} +18 z^{10} a^{-4} +6 z^{10} a^{-6} +21 z^9 a^{-1} +24 z^9 a^{-3} +7 z^9 a^{-5} +4 z^9 a^{-7} -9 z^8 a^{-2} -51 z^8 a^{-4} -19 z^8 a^{-6} +z^8 a^{-8} +22 z^8+17 a z^7-44 z^7 a^{-1} -105 z^7 a^{-3} -60 z^7 a^{-5} -16 z^7 a^{-7} +10 a^2 z^6-46 z^6 a^{-2} +17 z^6 a^{-4} +10 z^6 a^{-6} -4 z^6 a^{-8} -39 z^6+4 a^3 z^5-21 a z^5+26 z^5 a^{-1} +116 z^5 a^{-3} +87 z^5 a^{-5} +22 z^5 a^{-7} +a^4 z^4-7 a^2 z^4+58 z^4 a^{-2} +39 z^4 a^{-4} +14 z^4 a^{-6} +6 z^4 a^{-8} +19 z^4+7 a z^3-12 z^3 a^{-1} -47 z^3 a^{-3} -41 z^3 a^{-5} -13 z^3 a^{-7} +3 a^2 z^2-25 z^2 a^{-2} -27 z^2 a^{-4} -13 z^2 a^{-6} -4 z^2 a^{-8} -4 z^2+3 z a^{-1} +6 z a^{-3} +6 z a^{-5} +3 z a^{-7} -a^2+4 a^{-2} +5 a^{-4} +3 a^{-6} + a^{-8} +1}

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