K12a1087

Knot presentations

Dowker-Thistlethwaite code

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

Notes on presentations of K12a1087

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^6-4 q^5+10 q^4-18 q^3+27 q^2-33 q+36-34 q^{-1} +27 q^{-2} -19 q^{-3} +11 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^4-8 t^3+25 t^2-48 t+61-48 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^4-4 z^2+1}
Determinant	225
Signature	0
HOMFLY-PT polynomial	$z^{8}-2a^{2}z^{6}-2z^{6}a^{-2}+4z^{6}+a^{4}z^{4}-6a^{2}z^{4}-6z^{4}a^{-2}+z^{4}a^{-4}+7z^{4}+2a^{4}z^{2}-7a^{2}z^{2}-6z^{2}a^{-2}+2z^{2}a^{-4}+5z^{2}+2a^{4}-3a^{2}-a^{-2}+a^{-4}+2$
Kauffman polynomial	$3az^{11}+3z^{11}a^{-1}+9a^{2}z^{10}+8z^{10}a^{-2}+17z^{10}+12a^{3}z^{9}+16az^{9}+14z^{9}a^{-1}+10z^{9}a^{-3}+9a^{4}z^{8}-9a^{2}z^{8}-7z^{8}a^{-2}+8z^{8}a^{-4}-33z^{8}+4a^{5}z^{7}-26a^{3}z^{7}-53az^{7}-45z^{7}a^{-1}-18z^{7}a^{-3}+4z^{7}a^{-5}+a^{6}z^{6}-19a^{4}z^{6}-12a^{2}z^{6}-7z^{6}a^{-2}-16z^{6}a^{-4}+z^{6}a^{-6}+18z^{6}-7a^{5}z^{5}+22a^{3}z^{5}+58az^{5}+49z^{5}a^{-1}+12z^{5}a^{-3}-8z^{5}a^{-5}-2a^{6}z^{4}+14a^{4}z^{4}+25a^{2}z^{4}+11z^{4}a^{-2}+10z^{4}a^{-4}-2z^{4}a^{-6}+8z^{4}+2a^{5}z^{3}-13a^{3}z^{3}-26az^{3}-23z^{3}a^{-1}-8z^{3}a^{-3}+4z^{3}a^{-5}+a^{6}z^{2}-9a^{4}z^{2}-16a^{2}z^{2}-7z^{2}a^{-2}-4z^{2}a^{-4}+z^{2}a^{-6}-8z^{2}+4a^{3}z+6az+4za^{-1}+2za^{-3}+2a^{4}+3a^{2}+a^{-2}+a^{-4}+2$

Modifying This Page

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