K12a823

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a823

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^{12}-3 q^{11}+7 q^{10}-12 q^9+16 q^8-21 q^7+22 q^6-20 q^5+17 q^4-11 q^3+7 q^2-3 q+1}
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 -4 t^3+17 t^2-31 t+37-31 t^{-1} +17 t^{-2} -4 t^{-3} }
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 -4 z^6-7 z^4+z^2+1}
Determinant	141
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^6 a^{-4} -2 z^6 a^{-6} -z^6 a^{-8} +z^4 a^{-2} -z^4 a^{-4} -6 z^4 a^{-6} -2 z^4 a^{-8} +z^4 a^{-10} +2 z^2 a^{-2} +4 z^2 a^{-4} -6 z^2 a^{-6} -z^2 a^{-8} +2 z^2 a^{-10} +4 a^{-4} -3 a^{-6} - a^{-8} + a^{-10} }
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 z^{11} a^{-7} +z^{11} a^{-9} +3 z^{10} a^{-6} +7 z^{10} a^{-8} +4 z^{10} a^{-10} +5 z^9 a^{-5} +8 z^9 a^{-7} +9 z^9 a^{-9} +6 z^9 a^{-11} +5 z^8 a^{-4} +z^8 a^{-6} -16 z^8 a^{-8} -7 z^8 a^{-10} +5 z^8 a^{-12} +3 z^7 a^{-3} -11 z^7 a^{-5} -31 z^7 a^{-7} -38 z^7 a^{-9} -18 z^7 a^{-11} +3 z^7 a^{-13} +z^6 a^{-2} -14 z^6 a^{-4} -22 z^6 a^{-6} +9 z^6 a^{-8} +2 z^6 a^{-10} -13 z^6 a^{-12} +z^6 a^{-14} -8 z^5 a^{-3} +7 z^5 a^{-5} +44 z^5 a^{-7} +62 z^5 a^{-9} +25 z^5 a^{-11} -8 z^5 a^{-13} -3 z^4 a^{-2} +14 z^4 a^{-4} +37 z^4 a^{-6} +13 z^4 a^{-8} +5 z^4 a^{-10} +9 z^4 a^{-12} -3 z^4 a^{-14} +4 z^3 a^{-3} -3 z^3 a^{-5} -23 z^3 a^{-7} -43 z^3 a^{-9} -23 z^3 a^{-11} +4 z^3 a^{-13} +2 z^2 a^{-2} -12 z^2 a^{-4} -22 z^2 a^{-6} -6 z^2 a^{-8} -4 z^2 a^{-10} -4 z^2 a^{-12} +2 z^2 a^{-14} -z a^{-5} +6 z a^{-7} +14 z a^{-9} +7 z a^{-11} +4 a^{-4} +3 a^{-6} - a^{-8} - a^{-10} }

Modifying This Page

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