K12n635

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12n635

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 3 q^4-9 q^3+16 q^2-22 q+26-26 q^{-1} +23 q^{-2} -17 q^{-3} +10 q^{-4} -4 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+19 t^2-32 t+39-32 t^{-1} +19 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^6-3 z^4-3 z^2+1}
Determinant	157
Signature	0
HOMFLY-PT polynomial	$z^{8}-2a^{2}z^{6}-z^{6}a^{-2}+4z^{6}+a^{4}z^{4}-6a^{2}z^{4}-3z^{4}a^{-2}+5z^{4}+2a^{4}z^{2}-5a^{2}z^{2}-3z^{2}a^{-2}+z^{2}a^{-4}+2z^{2}+a^{4}-a^{2}-a^{-2}+a^{-4}+1$
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 3 a^2 z^{10}+3 z^{10}+8 a^3 z^9+17 a z^9+9 z^9 a^{-1} +8 a^4 z^8+15 a^2 z^8+9 z^8 a^{-2} +16 z^8+4 a^5 z^7-10 a^3 z^7-28 a z^7-11 z^7 a^{-1} +3 z^7 a^{-3} +a^6 z^6-17 a^4 z^6-47 a^2 z^6-13 z^6 a^{-2} -42 z^6-8 a^5 z^5-4 a^3 z^5+7 a z^5+9 z^5 a^{-1} +6 z^5 a^{-3} -2 a^6 z^4+13 a^4 z^4+37 a^2 z^4+15 z^4 a^{-2} +6 z^4 a^{-4} +31 z^4+5 a^5 z^3+5 a^3 z^3+2 a z^3-7 z^3 a^{-1} -9 z^3 a^{-3} +a^6 z^2-6 a^4 z^2-12 a^2 z^2-9 z^2 a^{-2} -6 z^2 a^{-4} -8 z^2-a^5 z-a^3 z+2 z a^{-1} +2 z a^{-3} +a^4+a^2+ a^{-2} + a^{-4} +1}

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