K12a1084

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1084

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}-3 q^9+7 q^8-12 q^7+17 q^6-21 q^5+22 q^4-21 q^3+17 q^2-12 q+8-3 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 t^4-8 t^3+20 t^2-28 t+31-28 t^{-1} +20 t^{-2} -8 t^{-3} + t^{-4} }
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 z^8-8 z^4-4 z^2+1}
Determinant	145
Signature	4
HOMFLY-PT 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^8 a^{-4} -2 z^6 a^{-2} +4 z^6 a^{-4} -2 z^6 a^{-6} -7 z^4 a^{-2} +4 z^4 a^{-4} -7 z^4 a^{-6} +z^4 a^{-8} +z^4-5 z^2 a^{-2} -5 z^2 a^{-6} +3 z^2 a^{-8} +3 z^2-2 a^{-4} + a^{-8} +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 2 z^{11} a^{-3} +2 z^{11} a^{-5} +4 z^{10} a^{-2} +11 z^{10} a^{-4} +7 z^{10} a^{-6} +3 z^9 a^{-1} +2 z^9 a^{-3} +10 z^9 a^{-5} +11 z^9 a^{-7} -14 z^8 a^{-2} -39 z^8 a^{-4} -13 z^8 a^{-6} +11 z^8 a^{-8} +z^8-13 z^7 a^{-1} -32 z^7 a^{-3} -57 z^7 a^{-5} -29 z^7 a^{-7} +9 z^7 a^{-9} +9 z^6 a^{-2} +39 z^6 a^{-4} -3 z^6 a^{-6} -22 z^6 a^{-8} +6 z^6 a^{-10} -5 z^6+17 z^5 a^{-1} +47 z^5 a^{-3} +80 z^5 a^{-5} +34 z^5 a^{-7} -13 z^5 a^{-9} +3 z^5 a^{-11} +5 z^4 a^{-2} -18 z^4 a^{-4} +11 z^4 a^{-6} +18 z^4 a^{-8} -6 z^4 a^{-10} +z^4 a^{-12} +9 z^4-7 z^3 a^{-1} -21 z^3 a^{-3} -51 z^3 a^{-5} -27 z^3 a^{-7} +8 z^3 a^{-9} -2 z^3 a^{-11} -2 z^2 a^{-2} +9 z^2 a^{-4} -7 z^2 a^{-6} -7 z^2 a^{-8} +3 z^2 a^{-10} -z^2 a^{-12} -7 z^2+4 z a^{-3} +12 z a^{-5} +8 z a^{-7} -2 a^{-4} + a^{-8} +2}

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