K12a1039

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1039

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^6-3 q^5+7 q^4-11 q^3+16 q^2-20 q+21-20 q^{-1} +16 q^{-2} -11 q^{-3} +7 q^{-4} -3 q^{-5} + q^{-6} }
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^4-7 t^3+17 t^2-27 t+33-27 t^{-1} +17 t^{-2} -7 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+z^6-5 z^4-6 z^2+1}
Determinant	137
Signature	0
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^8-2 a^2 z^6-2 z^6 a^{-2} +5 z^6+a^4 z^4-8 a^2 z^4-8 z^4 a^{-2} +z^4 a^{-4} +9 z^4+3 a^4 z^2-9 a^2 z^2-9 z^2 a^{-2} +3 z^2 a^{-4} +6 z^2+2 a^4-2 a^2-2 a^{-2} +2 a^{-4} +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 a z^{11}+z^{11} a^{-1} +3 a^2 z^{10}+3 z^{10} a^{-2} +6 z^{10}+5 a^3 z^9+6 a z^9+6 z^9 a^{-1} +5 z^9 a^{-3} +5 a^4 z^8-a^2 z^8-z^8 a^{-2} +5 z^8 a^{-4} -12 z^8+3 a^5 z^7-12 a^3 z^7-20 a z^7-20 z^7 a^{-1} -12 z^7 a^{-3} +3 z^7 a^{-5} +a^6 z^6-14 a^4 z^6-12 a^2 z^6-12 z^6 a^{-2} -14 z^6 a^{-4} +z^6 a^{-6} +6 z^6-8 a^5 z^5+11 a^3 z^5+21 a z^5+21 z^5 a^{-1} +11 z^5 a^{-3} -8 z^5 a^{-5} -3 a^6 z^4+13 a^4 z^4+20 a^2 z^4+20 z^4 a^{-2} +13 z^4 a^{-4} -3 z^4 a^{-6} +8 z^4+4 a^5 z^3-8 a^3 z^3-a z^3-z^3 a^{-1} -8 z^3 a^{-3} +4 z^3 a^{-5} +2 a^6 z^2-9 a^4 z^2-12 a^2 z^2-12 z^2 a^{-2} -9 z^2 a^{-4} +2 z^2 a^{-6} -2 z^2+a^3 z-3 a z-3 z a^{-1} +z a^{-3} +2 a^4+2 a^2+2 a^{-2} +2 a^{-4} +1}

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