K12a1053

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1053

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^5+4 q^4-10 q^3+19 q^2-28 q+35-37 q^{-1} +35 q^{-2} -28 q^{-3} +20 q^{-4} -11 q^{-5} +4 q^{-6} - q^{-7} }
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 2 t^4-10 t^3+27 t^2-48 t+59-48 t^{-1} +27 t^{-2} -10 t^{-3} +2 t^{-4} }
Conway polynomial	$2z^{8}+6z^{6}+7z^{4}+2z^{2}+1$
Determinant	233
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 a^2 z^8+z^8-a^4 z^6+4 a^2 z^6-z^6 a^{-2} +4 z^6-3 a^4 z^4+7 a^2 z^4-3 z^4 a^{-2} +6 z^4-4 a^4 z^2+7 a^2 z^2-3 z^2 a^{-2} +2 z^2-2 a^4+4 a^2-1}
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^3 z^{11}+3 a z^{11}+8 a^4 z^{10}+18 a^2 z^{10}+10 z^{10}+8 a^5 z^9+15 a^3 z^9+22 a z^9+15 z^9 a^{-1} +4 a^6 z^8-13 a^4 z^8-32 a^2 z^8+14 z^8 a^{-2} -z^8+a^7 z^7-21 a^5 z^7-55 a^3 z^7-63 a z^7-21 z^7 a^{-1} +9 z^7 a^{-3} -11 a^6 z^6-3 a^4 z^6+6 a^2 z^6-21 z^6 a^{-2} +4 z^6 a^{-4} -27 z^6-3 a^7 z^5+17 a^5 z^5+48 a^3 z^5+50 a z^5+10 z^5 a^{-1} -11 z^5 a^{-3} +z^5 a^{-5} +10 a^6 z^4+3 a^4 z^4-2 a^2 z^4+16 z^4 a^{-2} -4 z^4 a^{-4} +25 z^4+3 a^7 z^3-6 a^5 z^3-19 a^3 z^3-16 a z^3+z^3 a^{-1} +6 z^3 a^{-3} -z^3 a^{-5} -3 a^6 z^2+5 a^4 z^2+10 a^2 z^2-5 z^2 a^{-2} +z^2 a^{-4} -4 z^2-a^7 z+a^5 z+4 a^3 z+2 a z-z a^{-1} -z a^{-3} -2 a^4-4 a^2-1}

Modifying This Page

Read me first: Modifying Knot Pages See/edit the Large Knot Page master template. Back to the top.