This table contains the first few terms (degree 10 for 2 component, degree 6 for most 3 components) of the Gukov-Manolescu series for links under the column fk_polynomial. The braid and sign diagram used to compute the invariant are listed under braid and sign_diagram.

Snapshot changed; rerun validation.

knotinfo_id braid_length braid sign_diagram overall_x_powers fk_polynomial
L10n94{1;1} 11 {2,3,3,2,-3,1,-2,3,-2,-3,1} [[1, 1, -1, -1, -1, -1, -1, -1, -1, 1], [1, 1, 1, 1, 1, 1], [-1, -1, -1, -1, 1, -1]] 1 x1^-1*x2^-2*x3^2-x2^-1*x3-q^-3*x1^2*x2^-2*x3^2
L10n94{1;1} 11 {2,3,3,2,-3,1,-2,3,-2,-3,1} [[-1, 1, -1, -1, -1, -1, -1, -1, -1, 1], [1, 1, 1, 1, 1, -1], [-1, -1, -1, -1, 1, -1]] x1^(1/2) x1^-1*x2^-2*x3^2-x2^-1*x3-q^-3*x1^2*x2^-2*x3^2
L10n95{0;0} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[1, 1, -1, 1, -1, 1, -1, 1], [1, 1, 1, -1, 1, 1, 1, 1], [-1, -1, 1, -1, 1, -1]] 1 -q^-1*x1+q^-2*x1^2*x2^-1+x1^2*x3^-1-2*q^-1*x1^2+q^-2*x1^2*x3-q*x1^2*x2*x3^-1+x1^2*x2
L10n95{0;0} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[-1, 1, -1, 1, -1, 1, -1, 1], [1, 1, 1, -1, 1, 1, 1, -1], [-1, -1, 1, -1, 1, -1]] x1^(1/2) -q^-1*x1+q^-2*x1^2*x2^-1+x1^2*x3^-1-2*q^-1*x1^2+q^-2*x1^2*x3-q*x1^2*x2*x3^-1+x1^2*x2
L10n95{0;0} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[1, 1, 1, 1, 1, 1, -1, 1], [1, -1, -1, -1, -1, -1, 1, 1], [-1, -1, -1, -1, 1, -1]] 1 q^-2*x1^-1*x2^2-q^-1*x2+x2^2*x3^-1-q^-1*x2^2+q^-2*x2^2-q^-3*x2^2*x3-q^-1*x1*x2+q^-2*x1*x2*x3+x1*x2^2*x3^-1-2*q^-1*x1*x2^2+q^-2*x1*x2^2+q^-2*x1*x2^2*x3-q^-3*x1*x2^2*x3-q^-4*x1*x2^2*x3+q^-5*x1*x2^2*x3^2-q^-1*x1^2*x2+q^-2*x1^2*x2*x3+q^-3*x1^2*x2*x3-q^-4*x1^2*x2*x3^2+x1^2*x2^2*x3^-1-3*q^-1*x1^2*x2^2+q^-2*x1^2*x2^2*x3+q^-3*x1^2*x2^2*x3-q^-4*x1^2*x2^2*x3-q^-5*x1^2*x2^2*x3-q^-4*x1^2*x2^2*x3^2+q^-5*x1^2*x2^2*x3^2+q^-6*x1^2*x2^2*x3^2+q^-7*x1^2*x2^2*x3^2
L10n95{0;0} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[-1, 1, 1, 1, 1, 1, -1, 1], [1, -1, -1, -1, -1, -1, 1, -1], [-1, -1, -1, -1, 1, -1]] 1 q^-2*x1^-1*x2^2-q^-1*x2+x2^2*x3^-1-q^-1*x2^2+q^-2*x2^2-q^-3*x2^2*x3-q^-1*x1*x2+q^-2*x1*x2*x3+x1*x2^2*x3^-1-2*q^-1*x1*x2^2+q^-2*x1*x2^2+q^-2*x1*x2^2*x3-q^-3*x1*x2^2*x3-q^-4*x1*x2^2*x3+q^-5*x1*x2^2*x3^2-q^-1*x1^2*x2+q^-2*x1^2*x2*x3+q^-3*x1^2*x2*x3-q^-4*x1^2*x2*x3^2+x1^2*x2^2*x3^-1-3*q^-1*x1^2*x2^2+q^-2*x1^2*x2^2*x3+q^-3*x1^2*x2^2*x3-q^-4*x1^2*x2^2*x3-q^-5*x1^2*x2^2*x3-q^-4*x1^2*x2^2*x3^2+q^-5*x1^2*x2^2*x3^2+q^-6*x1^2*x2^2*x3^2+q^-7*x1^2*x2^2*x3^2
L10n95{0;0} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[1, 1, -1, -1, -1, 1, -1, 1], [1, -1, -1, -1, -1, -1, 1, 1], [-1, -1, 1, -1, 1, -1]] x1^(1/2) x1^-1*x3^2+x1^-1*x2*x3^2+q^-1*x1^-1*x2*x3^2+x1^-1*x2^2*x3^2+q^-1*x1^-1*x2^2*x3^2+q^-2*x1^-1*x2^2*x3^2+x2^-1*x3^2-q^-1*x3+q*x3^2+2*x3^2-q^-1*x3^2-q^-1*x2*x3+q^2*x2*x3^2+2*q*x2*x3^2+3*x2*x3^2-q^-1*x2^2*x3+q^3*x2^2*x3^2+2*q^2*x2^2*x3^2+3*q*x2^2*x3^2+4*x2^2*x3^2+q^-1*x2^2*x3^2+q^-2*x2^2*x3^2+x1*x2^-1*x3^2-q^-1*x1*x3+q^2*x1*x3^2+2*q*x1*x3^2+2*x1*x3^2-q^-1*x1*x3^2+q^-2*x1*x3^2-x1*x2*x3-q^-1*x1*x2*x3+q^4*x1*x2*x3^2+2*q^3*x1*x2*x3^2+4*q^2*x1*x2*x3^2+4*q*x1*x2*x3^2+2*x1*x2*x3^2+q^-2*x1*x2*x3^2-q*x1*x2^2*x3-x1*x2^2*x3-q^-1*x1*x2^2*x3+q^6*x1*x2^2*x3^2+2*q^5*x1*x2^2*x3^2+4*q^4*x1*x2^2*x3^2+6*q^3*x1*x2^2*x3^2+7*q^2*x1*x2^2*x3^2+5*q*x1*x2^2*x3^2+4*x1*x2^2*x3^2+q^-1*x1*x2^2*x3^2+2*q^-2*x1*x2^2*x3^2+x1^2*x2^-1*x3^2-q^-1*x1^2*x3+q^3*x1^2*x3^2+2*q^2*x1^2*x3^2+2*q*x1^2*x3^2+2*x1^2*x3^2-q^-1*x1^2*x3^2+q^-2*x1^2*x3^2-q*x1^2*x2*x3-x1^2*x2*x3-q^-1*x1^2*x2*x3+q^6*x1^2*x2*x3^2+2*q^5*x1^2*x2*x3^2+4*q^4*x1^2*x2*x3^2+5*q^3*x1^2*x2*x3^2+6*q^2*x1^2*x2*x3^2+3*q*x1^2*x2*x3^2+2*x1^2*x2*x3^2+q^-1*x1^2*x2*x3^2+q^-2*x1^2*x2*x3^2-q^3*x1^2*x2^2*x3-q^2*x1^2*x2^2*x3-2*q*x1^2*x2^2*x3-x1^2*x2^2*x3-q^-1*x1^2*x2^2*x3+q^9*x1^2*x2^2*x3^2+2*q^8*x1^2*x2^2*x3^2+4*q^7*x1^2*x2^2*x3^2+7*q^6*x1^2*x2^2*x3^2+9*q^5*x1^2*x2^2*x3^2+11*q^4*x1^2*x2^2*x3^2+10*q^3*x1^2*x2^2*x3^2+9*q^2*x1^2*x2^2*x3^2+5*q*x1^2*x2^2*x3^2+5*x1^2*x2^2*x3^2+2*q^-1*x1^2*x2^2*x3^2+2*q^-2*x1^2*x2^2*x3^2
L10n95{0;0} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[-1, 1, -1, -1, -1, 1, -1, 1], [1, -1, -1, -1, -1, -1, 1, -1], [-1, -1, 1, -1, 1, -1]] 1 x1^-1*x3^2+x1^-1*x2*x3^2+q^-1*x1^-1*x2*x3^2+x1^-1*x2^2*x3^2+q^-1*x1^-1*x2^2*x3^2+q^-2*x1^-1*x2^2*x3^2+x2^-1*x3^2-q^-1*x3+q*x3^2+2*x3^2-q^-1*x3^2-q^-1*x2*x3+q^2*x2*x3^2+2*q*x2*x3^2+3*x2*x3^2-q^-1*x2^2*x3+q^3*x2^2*x3^2+2*q^2*x2^2*x3^2+3*q*x2^2*x3^2+4*x2^2*x3^2+q^-1*x2^2*x3^2+q^-2*x2^2*x3^2+x1*x2^-1*x3^2-q^-1*x1*x3+q^2*x1*x3^2+2*q*x1*x3^2+2*x1*x3^2-q^-1*x1*x3^2+q^-2*x1*x3^2-x1*x2*x3-q^-1*x1*x2*x3+q^4*x1*x2*x3^2+2*q^3*x1*x2*x3^2+4*q^2*x1*x2*x3^2+4*q*x1*x2*x3^2+2*x1*x2*x3^2+q^-2*x1*x2*x3^2-q*x1*x2^2*x3-x1*x2^2*x3-q^-1*x1*x2^2*x3+q^6*x1*x2^2*x3^2+2*q^5*x1*x2^2*x3^2+4*q^4*x1*x2^2*x3^2+6*q^3*x1*x2^2*x3^2+7*q^2*x1*x2^2*x3^2+5*q*x1*x2^2*x3^2+4*x1*x2^2*x3^2+q^-1*x1*x2^2*x3^2+2*q^-2*x1*x2^2*x3^2+x1^2*x2^-1*x3^2-q^-1*x1^2*x3+q^3*x1^2*x3^2+2*q^2*x1^2*x3^2+2*q*x1^2*x3^2+2*x1^2*x3^2-q^-1*x1^2*x3^2+q^-2*x1^2*x3^2-q*x1^2*x2*x3-x1^2*x2*x3-q^-1*x1^2*x2*x3+q^6*x1^2*x2*x3^2+2*q^5*x1^2*x2*x3^2+4*q^4*x1^2*x2*x3^2+5*q^3*x1^2*x2*x3^2+6*q^2*x1^2*x2*x3^2+3*q*x1^2*x2*x3^2+2*x1^2*x2*x3^2+q^-1*x1^2*x2*x3^2+q^-2*x1^2*x2*x3^2-q^3*x1^2*x2^2*x3-q^2*x1^2*x2^2*x3-2*q*x1^2*x2^2*x3-x1^2*x2^2*x3-q^-1*x1^2*x2^2*x3+q^9*x1^2*x2^2*x3^2+2*q^8*x1^2*x2^2*x3^2+4*q^7*x1^2*x2^2*x3^2+7*q^6*x1^2*x2^2*x3^2+9*q^5*x1^2*x2^2*x3^2+11*q^4*x1^2*x2^2*x3^2+10*q^3*x1^2*x2^2*x3^2+9*q^2*x1^2*x2^2*x3^2+5*q*x1^2*x2^2*x3^2+5*x1^2*x2^2*x3^2+2*q^-1*x1^2*x2^2*x3^2+2*q^-2*x1^2*x2^2*x3^2
L10n95{0;1} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[1, 1, -1, 1, -1, 1, -1, 1], [1, 1, 1, -1, 1, 1, 1, 1], [-1, -1, 1, -1, 1, -1]] 1 -q^-1*x1+q^-2*x1^2*x2^-1+x1^2*x3^-1-2*q^-1*x1^2+q^-2*x1^2*x3-q*x1^2*x2*x3^-1+x1^2*x2
L10n95{0;1} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[-1, 1, -1, 1, -1, 1, -1, 1], [1, 1, 1, -1, 1, 1, 1, -1], [-1, -1, 1, -1, 1, -1]] 1 -q^-1*x1+q^-2*x1^2*x2^-1+x1^2*x3^-1-2*q^-1*x1^2+q^-2*x1^2*x3-q*x1^2*x2*x3^-1+x1^2*x2
L10n95{0;1} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[1, 1, 1, 1, 1, 1, -1, 1], [1, -1, -1, -1, -1, -1, 1, 1], [-1, -1, -1, -1, 1, -1]] 1 q^-2*x1^-1*x2^2-q^-1*x2+x2^2*x3^-1-q^-1*x2^2+q^-2*x2^2-q^-3*x2^2*x3-q^-1*x1*x2+q^-2*x1*x2*x3+x1*x2^2*x3^-1-2*q^-1*x1*x2^2+q^-2*x1*x2^2+q^-2*x1*x2^2*x3-q^-3*x1*x2^2*x3-q^-4*x1*x2^2*x3+q^-5*x1*x2^2*x3^2-q^-1*x1^2*x2+q^-2*x1^2*x2*x3+q^-3*x1^2*x2*x3-q^-4*x1^2*x2*x3^2+x1^2*x2^2*x3^-1-3*q^-1*x1^2*x2^2+q^-2*x1^2*x2^2*x3+q^-3*x1^2*x2^2*x3-q^-4*x1^2*x2^2*x3-q^-5*x1^2*x2^2*x3-q^-4*x1^2*x2^2*x3^2+q^-5*x1^2*x2^2*x3^2+q^-6*x1^2*x2^2*x3^2+q^-7*x1^2*x2^2*x3^2
L10n95{0;1} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[-1, 1, 1, 1, 1, 1, -1, 1], [1, -1, -1, -1, -1, -1, 1, -1], [-1, -1, -1, -1, 1, -1]] x1^(1/2) q^-2*x1^-1*x2^2-q^-1*x2+x2^2*x3^-1-q^-1*x2^2+q^-2*x2^2-q^-3*x2^2*x3-q^-1*x1*x2+q^-2*x1*x2*x3+x1*x2^2*x3^-1-2*q^-1*x1*x2^2+q^-2*x1*x2^2+q^-2*x1*x2^2*x3-q^-3*x1*x2^2*x3-q^-4*x1*x2^2*x3+q^-5*x1*x2^2*x3^2-q^-1*x1^2*x2+q^-2*x1^2*x2*x3+q^-3*x1^2*x2*x3-q^-4*x1^2*x2*x3^2+x1^2*x2^2*x3^-1-3*q^-1*x1^2*x2^2+q^-2*x1^2*x2^2*x3+q^-3*x1^2*x2^2*x3-q^-4*x1^2*x2^2*x3-q^-5*x1^2*x2^2*x3-q^-4*x1^2*x2^2*x3^2+q^-5*x1^2*x2^2*x3^2+q^-6*x1^2*x2^2*x3^2+q^-7*x1^2*x2^2*x3^2
L10n95{0;1} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[1, 1, -1, -1, -1, 1, -1, 1], [1, -1, -1, -1, -1, -1, 1, 1], [-1, -1, 1, -1, 1, -1]] 1 x1^-1*x3^2+x1^-1*x2*x3^2+q^-1*x1^-1*x2*x3^2+x1^-1*x2^2*x3^2+q^-1*x1^-1*x2^2*x3^2+q^-2*x1^-1*x2^2*x3^2+x2^-1*x3^2-q^-1*x3+q*x3^2+2*x3^2-q^-1*x3^2-q^-1*x2*x3+q^2*x2*x3^2+2*q*x2*x3^2+3*x2*x3^2-q^-1*x2^2*x3+q^3*x2^2*x3^2+2*q^2*x2^2*x3^2+3*q*x2^2*x3^2+4*x2^2*x3^2+q^-1*x2^2*x3^2+q^-2*x2^2*x3^2+x1*x2^-1*x3^2-q^-1*x1*x3+q^2*x1*x3^2+2*q*x1*x3^2+2*x1*x3^2-q^-1*x1*x3^2+q^-2*x1*x3^2-x1*x2*x3-q^-1*x1*x2*x3+q^4*x1*x2*x3^2+2*q^3*x1*x2*x3^2+4*q^2*x1*x2*x3^2+4*q*x1*x2*x3^2+2*x1*x2*x3^2+q^-2*x1*x2*x3^2-q*x1*x2^2*x3-x1*x2^2*x3-q^-1*x1*x2^2*x3+q^6*x1*x2^2*x3^2+2*q^5*x1*x2^2*x3^2+4*q^4*x1*x2^2*x3^2+6*q^3*x1*x2^2*x3^2+7*q^2*x1*x2^2*x3^2+5*q*x1*x2^2*x3^2+4*x1*x2^2*x3^2+q^-1*x1*x2^2*x3^2+2*q^-2*x1*x2^2*x3^2+x1^2*x2^-1*x3^2-q^-1*x1^2*x3+q^3*x1^2*x3^2+2*q^2*x1^2*x3^2+2*q*x1^2*x3^2+2*x1^2*x3^2-q^-1*x1^2*x3^2+q^-2*x1^2*x3^2-q*x1^2*x2*x3-x1^2*x2*x3-q^-1*x1^2*x2*x3+q^6*x1^2*x2*x3^2+2*q^5*x1^2*x2*x3^2+4*q^4*x1^2*x2*x3^2+5*q^3*x1^2*x2*x3^2+6*q^2*x1^2*x2*x3^2+3*q*x1^2*x2*x3^2+2*x1^2*x2*x3^2+q^-1*x1^2*x2*x3^2+q^-2*x1^2*x2*x3^2-q^3*x1^2*x2^2*x3-q^2*x1^2*x2^2*x3-2*q*x1^2*x2^2*x3-x1^2*x2^2*x3-q^-1*x1^2*x2^2*x3+q^9*x1^2*x2^2*x3^2+2*q^8*x1^2*x2^2*x3^2+4*q^7*x1^2*x2^2*x3^2+7*q^6*x1^2*x2^2*x3^2+9*q^5*x1^2*x2^2*x3^2+11*q^4*x1^2*x2^2*x3^2+10*q^3*x1^2*x2^2*x3^2+9*q^2*x1^2*x2^2*x3^2+5*q*x1^2*x2^2*x3^2+5*x1^2*x2^2*x3^2+2*q^-1*x1^2*x2^2*x3^2+2*q^-2*x1^2*x2^2*x3^2
L10n95{0;1} 11 {-2,-3,1,-2,3,3,-2,-2,-2,-3,1} [[-1, 1, -1, -1, -1, 1, -1, 1], [1, -1, -1, -1, -1, -1, 1, -1], [-1, -1, 1, -1, 1, -1]] x1^(1/2) x1^-1*x3^2+x1^-1*x2*x3^2+q^-1*x1^-1*x2*x3^2+x1^-1*x2^2*x3^2+q^-1*x1^-1*x2^2*x3^2+q^-2*x1^-1*x2^2*x3^2+x2^-1*x3^2-q^-1*x3+q*x3^2+2*x3^2-q^-1*x3^2-q^-1*x2*x3+q^2*x2*x3^2+2*q*x2*x3^2+3*x2*x3^2-q^-1*x2^2*x3+q^3*x2^2*x3^2+2*q^2*x2^2*x3^2+3*q*x2^2*x3^2+4*x2^2*x3^2+q^-1*x2^2*x3^2+q^-2*x2^2*x3^2+x1*x2^-1*x3^2-q^-1*x1*x3+q^2*x1*x3^2+2*q*x1*x3^2+2*x1*x3^2-q^-1*x1*x3^2+q^-2*x1*x3^2-x1*x2*x3-q^-1*x1*x2*x3+q^4*x1*x2*x3^2+2*q^3*x1*x2*x3^2+4*q^2*x1*x2*x3^2+4*q*x1*x2*x3^2+2*x1*x2*x3^2+q^-2*x1*x2*x3^2-q*x1*x2^2*x3-x1*x2^2*x3-q^-1*x1*x2^2*x3+q^6*x1*x2^2*x3^2+2*q^5*x1*x2^2*x3^2+4*q^4*x1*x2^2*x3^2+6*q^3*x1*x2^2*x3^2+7*q^2*x1*x2^2*x3^2+5*q*x1*x2^2*x3^2+4*x1*x2^2*x3^2+q^-1*x1*x2^2*x3^2+2*q^-2*x1*x2^2*x3^2+x1^2*x2^-1*x3^2-q^-1*x1^2*x3+q^3*x1^2*x3^2+2*q^2*x1^2*x3^2+2*q*x1^2*x3^2+2*x1^2*x3^2-q^-1*x1^2*x3^2+q^-2*x1^2*x3^2-q*x1^2*x2*x3-x1^2*x2*x3-q^-1*x1^2*x2*x3+q^6*x1^2*x2*x3^2+2*q^5*x1^2*x2*x3^2+4*q^4*x1^2*x2*x3^2+5*q^3*x1^2*x2*x3^2+6*q^2*x1^2*x2*x3^2+3*q*x1^2*x2*x3^2+2*x1^2*x2*x3^2+q^-1*x1^2*x2*x3^2+q^-2*x1^2*x2*x3^2-q^3*x1^2*x2^2*x3-q^2*x1^2*x2^2*x3-2*q*x1^2*x2^2*x3-x1^2*x2^2*x3-q^-1*x1^2*x2^2*x3+q^9*x1^2*x2^2*x3^2+2*q^8*x1^2*x2^2*x3^2+4*q^7*x1^2*x2^2*x3^2+7*q^6*x1^2*x2^2*x3^2+9*q^5*x1^2*x2^2*x3^2+11*q^4*x1^2*x2^2*x3^2+10*q^3*x1^2*x2^2*x3^2+9*q^2*x1^2*x2^2*x3^2+5*q*x1^2*x2^2*x3^2+5*x1^2*x2^2*x3^2+2*q^-1*x1^2*x2^2*x3^2+2*q^-2*x1^2*x2^2*x3^2
L10n95{1;0} 10 {-1,2,-1,-2,-2,-2,1,-2,-2,-2} [[1, -1, 1, 1, -1, 1], [-1, 1, -1, -1, 1, -1, 1, -1], [1, -1, 1, 1, -1, 1]] 1 -q^-2*x1*x3-q^-2*x1*x3^2+q^-3*x1*x2*x3^2-x1^2*x2^-1*x3^2-q^-2*x1^2*x3+q^-1*x1^2*x3^2-q^-2*x1^2*x3^2+q^-3*x1^2*x2*x3+2*q^-3*x1^2*x2*x3^2-q^-4*x1^2*x2^2*x3^2
L10n95{1;0} 10 {-1,2,-1,-2,-2,-2,1,-2,-2,-2} [[-1, -1, 1, 1, -1, 1], [-1, -1, -1, -1, 1, -1, 1, -1], [1, -1, -1, 1, -1, 1]] x2^(1/2) -q^-2*x1*x3-q^-2*x1*x3^2+q^-3*x1*x2*x3^2-x1^2*x2^-1*x3^2-q^-2*x1^2*x3+q^-1*x1^2*x3^2-q^-2*x1^2*x3^2+q^-3*x1^2*x2*x3+2*q^-3*x1^2*x2*x3^2-q^-4*x1^2*x2^2*x3^2
L10n95{1;0} 10 {-1,2,-1,-2,-2,-2,1,-2,-2,-2} [[1, -1, -1, 1, -1, 1], [-1, 1, 1, -1, 1, -1, -1, -1], [-1, -1, -1, -1, -1, -1]] 1 -x1^-1*x2^2*x3^-1+q^-1*x1^-1*x2^2-q^-2*x2+q^-1*x2^2*x3^-1-2*q^-2*x2^2+q^-3*x2^2*x3+q^-3*x1*x2^2
L10n95{1;1} 12 {2,3,3,2,3,-4,3,4,4,1,-2,1} [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]] x1^(1/2) -x1^-3*x2^2*x3^2+q*x1^-2*x2*x3^2+q*x1^-2*x2^2*x3+2*q*x1^-2*x2^2*x3^2-q^2*x1^-1*x2*x3-q^2*x1^-1*x2*x3^2-q^2*x1^-1*x2^2*x3+q^3*x1^-1*x2^2*x3^2-q^2*x1^-1*x2^2*x3^2-q^4*x2^2*x3^2
L10n95{1;1} 12 {2,3,3,2,3,-4,3,4,4,1,-2,1} [[-1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, -1], [1, 1, 1, 1, 1, 1]] 1 -x1^-3*x2^2*x3^2+q*x1^-2*x2*x3^2+q*x1^-2*x2^2*x3+2*q*x1^-2*x2^2*x3^2-q^2*x1^-1*x2*x3-q^2*x1^-1*x2*x3^2-q^2*x1^-1*x2^2*x3+q^3*x1^-1*x2^2*x3^2-q^2*x1^-1*x2^2*x3^2-q^4*x2^2*x3^2
L10n95{1;1} 12 {2,3,3,2,3,-4,3,4,4,1,-2,1} [[1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, 1, 1, 1]] x1^(1/2) q*x1^-1*x2^2-q^2*x2-x2^2*x3^-1-q^2*x2^2+q*x2^2+q^3*x2^2*x3+q*x1*x2*x3^-1-q^2*x1*x2+q^-2*x1*x2^2*x3^-2+q*x1*x2^2*x3^-1-x1*x2^2*x3^-1-q^-1*x1*x2^2*x3^-1-2*q^2*x1*x2^2+q*x1*x2^2+q^3*x1*x2^2*x3-q^-1*x1^2*x2*x3^-2+q*x1^2*x2*x3^-1+x1^2*x2*x3^-1-q^2*x1^2*x2-q^-5*x1^2*x2^2*x3^-3-q^-1*x1^2*x2^2*x3^-2+q^-2*x1^2*x2^2*x3^-2+q^-3*x1^2*x2^2*x3^-2+q^-4*x1^2*x2^2*x3^-2+q*x1^2*x2^2*x3^-1+x1^2*x2^2*x3^-1-q^-1*x1^2*x2^2*x3^-1-q^-2*x1^2*x2^2*x3^-1-3*q^2*x1^2*x2^2+q^3*x1^2*x2^2*x3
L10n95{1;1} 12 {2,3,3,2,3,-4,3,4,4,1,-2,1} [[-1, 1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1], [1, 1, 1, 1, 1, -1], [1, 1, 1, 1, 1, 1]] 1 q*x1^-1*x2^2-q^2*x2-x2^2*x3^-1-q^2*x2^2+q*x2^2+q^3*x2^2*x3+q*x1*x2*x3^-1-q^2*x1*x2+q^-2*x1*x2^2*x3^-2+q*x1*x2^2*x3^-1-x1*x2^2*x3^-1-q^-1*x1*x2^2*x3^-1-2*q^2*x1*x2^2+q*x1*x2^2+q^3*x1*x2^2*x3-q^-1*x1^2*x2*x3^-2+q*x1^2*x2*x3^-1+x1^2*x2*x3^-1-q^2*x1^2*x2-q^-5*x1^2*x2^2*x3^-3-q^-1*x1^2*x2^2*x3^-2+q^-2*x1^2*x2^2*x3^-2+q^-3*x1^2*x2^2*x3^-2+q^-4*x1^2*x2^2*x3^-2+q*x1^2*x2^2*x3^-1+x1^2*x2^2*x3^-1-q^-1*x1^2*x2^2*x3^-1-q^-2*x1^2*x2^2*x3^-1-3*q^2*x1^2*x2^2+q^3*x1^2*x2^2*x3
L10n95{1;1} 12 {2,3,3,2,3,-4,3,4,4,1,-2,1} [[1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, -1, 1, 1]] x1^(1/2) q*x1^-1*x3^2-x2^-1*x3^2-q^2*x3-q^2*x3^2+q*x3^2+q^3*x2*x3^2+q^-2*x1*x2^-2*x3^2+q*x1*x2^-1*x3+q*x1*x2^-1*x3^2-x1*x2^-1*x3^2-q^-1*x1*x2^-1*x3^2-q^2*x1*x3-2*q^2*x1*x3^2+q*x1*x3^2+q^3*x1*x2*x3^2-q^-5*x1^2*x2^-3*x3^2-q^-1*x1^2*x2^-2*x3-q^-1*x1^2*x2^-2*x3^2+q^-2*x1^2*x2^-2*x3^2+q^-3*x1^2*x2^-2*x3^2+q^-4*x1^2*x2^-2*x3^2+q*x1^2*x2^-1*x3+x1^2*x2^-1*x3+q*x1^2*x2^-1*x3^2+x1^2*x2^-1*x3^2-q^-1*x1^2*x2^-1*x3^2-q^-2*x1^2*x2^-1*x3^2-q^2*x1^2*x3-2*q^2*x1^2*x3^2-q*x1^2*x3^2+q^4*x1^2*x2^2*x3^2+q^3*x1^2*x2^2*x3^2
L10n95{1;1} 12 {2,3,3,2,3,-4,3,4,4,1,-2,1} [[-1, 1, -1, -1, -1, 1, 1, 1, 1, 1, -1, 1], [1, 1, 1, 1, 1, -1], [1, 1, 1, -1, 1, 1]] 1 q*x1^-1*x3^2-x2^-1*x3^2-q^2*x3-q^2*x3^2+q*x3^2+q^3*x2*x3^2+q^-2*x1*x2^-2*x3^2+q*x1*x2^-1*x3+q*x1*x2^-1*x3^2-x1*x2^-1*x3^2-q^-1*x1*x2^-1*x3^2-q^2*x1*x3-2*q^2*x1*x3^2+q*x1*x3^2+q^3*x1*x2*x3^2-q^-5*x1^2*x2^-3*x3^2-q^-1*x1^2*x2^-2*x3-q^-1*x1^2*x2^-2*x3^2+q^-2*x1^2*x2^-2*x3^2+q^-3*x1^2*x2^-2*x3^2+q^-4*x1^2*x2^-2*x3^2+q*x1^2*x2^-1*x3+x1^2*x2^-1*x3+q*x1^2*x2^-1*x3^2+x1^2*x2^-1*x3^2-q^-1*x1^2*x2^-1*x3^2-q^-2*x1^2*x2^-1*x3^2-q^2*x1^2*x3-3*q^2*x1^2*x3^2+q^3*x1^2*x2*x3^2
L10n95{1;1} 12 {2,3,3,2,3,-4,3,4,4,1,-2,1} [[1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1], [1, 1, 1, 1, 1, 1], [1, 1, 1, -1, 1, 1]] 1 -q^2*x1+q*x1^2*x2^-1+q*x1^2*x3^-1-2*q^2*x1^2+q^3*x1^2*x3+q^3*x1^2*x2-q^4*x1^2*x2*x3
L10n95{1;1} 12 {2,3,3,2,3,-4,3,4,4,1,-2,1} [[-1, 1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1], [1, 1, 1, 1, 1, -1], [1, 1, 1, -1, 1, 1]] 1 -q^2*x1+q*x1^2*x2^-1+q*x1^2*x3^-1-2*q^2*x1^2+q^3*x1^2*x3+q^3*x1^2*x2-q^4*x1^2*x2*x3

25 rows shown · 1125 matching rows · Gukov-Manolescu series (F_K) for most nice Links of 10 crossings

First page

Metadata and schema

Provenance
Unknown / not supplied
Authors
Unknown / not supplied
Citations
['Davide Passaro, Lara San Martín Suárez. "The Gukov-Manolescu Series for Links." In preparation.']
Bibtex
Unknown / not supplied
License
Unknown / not supplied
Methodology
Legacy schema requires audit. Source payloads are preserved; name-based joins are uncertified.
Completeness
Unknown / not supplied

Name-based joins are uncertified.

ColumnTypeDescription
knotinfo_idstringKnotInfo identifier
braid_lengthintLength of the braid used for the computation
braidmathematica_short_codeBraid word used for the computation
sign_diagramstringSign diagram used for the computation (list of sign sequences per component)
overall_x_powersmathematica_short_codeOverall x powers per component
fk_polynomialmathematica_short_codeFirst terms of the F_K series (Mathematica format)

Schema version: aa1636480dea6070739c67d8d871d8793da3740719d241df1b7061303bae5f1e · Data version: unversioned-synapse

REST API

JSON rows for the current filters: GET https://topology.fyi/api/v1/datasets/fk_links_table_10/rows?raw=1

Schema: /api/v1/datasets/fk_links_table_10/schema

curl "https://topology.fyi/api/v1/datasets/fk_links_table_10/rows?raw=1"

Citation

Please cite this dataset using:

Davide Passaro, Lara San Martín Suárez. "The Gukov-Manolescu Series for Links." In preparation.