K12a1093

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1093

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^7-9 q^6+17 q^5-25 q^4+30 q^3-33 q^2+31 q-24+18 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 -t^4+8 t^3-25 t^2+44 t-51+44 t^{-1} -25 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+3 z^4+1}
Determinant	207
Signature	2
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^{-2} -4 z^6 a^{-2} +2 z^6 a^{-4} +2 z^6-a^2 z^4-7 z^4 a^{-2} +6 z^4 a^{-4} -z^4 a^{-6} +6 z^4-2 a^2 z^2-7 z^2 a^{-2} +5 z^2 a^{-4} -2 z^2 a^{-6} +6 z^2-a^2-3 a^{-2} + a^{-4} +4}
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^{-1} +3 z^{11} a^{-3} +17 z^{10} a^{-2} +10 z^{10} a^{-4} +7 z^{10}+7 a z^9+10 z^9 a^{-1} +17 z^9 a^{-3} +14 z^9 a^{-5} +4 a^2 z^8-42 z^8 a^{-2} -14 z^8 a^{-4} +12 z^8 a^{-6} -12 z^8+a^3 z^7-18 a z^7-50 z^7 a^{-1} -69 z^7 a^{-3} -30 z^7 a^{-5} +8 z^7 a^{-7} -12 a^2 z^6+24 z^6 a^{-2} -2 z^6 a^{-4} -19 z^6 a^{-6} +4 z^6 a^{-8} -9 z^6-3 a^3 z^5+9 a z^5+54 z^5 a^{-1} +84 z^5 a^{-3} +31 z^5 a^{-5} -10 z^5 a^{-7} +z^5 a^{-9} +11 a^2 z^4+8 z^4 a^{-2} +16 z^4 a^{-4} +10 z^4 a^{-6} -5 z^4 a^{-8} +18 z^4+3 a^3 z^3-22 z^3 a^{-1} -35 z^3 a^{-3} -13 z^3 a^{-5} +2 z^3 a^{-7} -z^3 a^{-9} -5 a^2 z^2-9 z^2 a^{-2} -6 z^2 a^{-4} -z^2 a^{-6} +z^2 a^{-8} -10 z^2-a^3 z-a z+z a^{-1} +z a^{-3} +a^2+3 a^{-2} + a^{-4} +4}

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