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
L10a18{0} 10 {-1,-1,2,-1,-1,-3,2,2,-1,-3} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [-1, 1, -1, 1]] 1 -q^-2*x1^2-q^-2*x1^2*x2-q^-2*x1^2*x2^2
L10a18{0} 10 {-1,-1,2,-1,-1,-3,2,2,-1,-3} [[-1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1], [-1, 1, -1, 1]] 1 -q^-2*x1^2-q^-2*x1^2*x2-q^-2*x1^2*x2^2
L10a18{1} 10 {-1,-1,2,-1,-1,-3,2,2,-1,-3} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [-1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^-2*x1^2-q^-2*x1^2*x2-q^-2*x1^2*x2^2
L10a18{1} 10 {-1,-1,2,-1,-1,-3,2,2,-1,-3} [[-1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1], [-1, 1, -1, 1]] 1 -q^-2*x1^2-q^-2*x1^2*x2-q^-2*x1^2*x2^2
L10a2{0} 10 {-1,2,-1,2,-1,-3,2,-3,-3,-3} [[1, -1, 1, -1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^-2*x2^2-q^-2*x1*x2^2-q^-2*x1^2*x2^2
L10a2{0} 10 {-1,2,-1,2,-1,-3,2,-3,-3,-3} [[-1, -1, 1, -1], [-1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^-2*x2^2-q^-2*x1*x2^2-q^-2*x1^2*x2^2
L10a2{1} 10 {-1,2,-1,2,-1,-3,2,-3,-3,-3} [[1, -1, 1, -1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^-2*x2^2-q^-2*x1*x2^2-q^-2*x1^2*x2^2
L10a2{1} 10 {-1,2,-1,2,-1,-3,2,-3,-3,-3} [[-1, -1, 1, -1], [-1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^-2*x2^2-q^-2*x1*x2^2-q^-2*x1^2*x2^2
L10a20{0} 12 {1,-2,-3,-2,1,1,-2,1,-2,3,-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 -x2^2-x1*x2^2-x1^2*x2^2
L10a20{0} 12 {1,-2,-3,-2,1,1,-2,1,-2,3,-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 -x2^2-x1*x2^2-x1^2*x2^2
L10a20{1} 10 {-1,2,2,-1,-3,2,2,-1,-3,2} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [-1, 1, -1, 1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a20{1} 10 {-1,2,2,-1,-3,2,2,-1,-3,2} [[-1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1], [-1, 1, -1, 1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a21{0} 10 {1,-2,1,-2,3,-2,3,3,-2,3} [[1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a21{0} 10 {1,-2,1,-2,3,-2,3,3,-2,3} [[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a21{1} 10 {1,-2,1,-2,3,-2,3,3,-2,3} [[1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a21{1} 10 {1,-2,1,-2,3,-2,3,3,-2,3} [[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a22{0} 10 {1,-2,1,3,-2,3,3,-2,1,3} [[1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q*x1^2-q*x1^2*x2-q*x1^2*x2^2
L10a22{0} 10 {1,-2,1,3,-2,3,3,-2,1,3} [[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q*x1^2-q*x1^2*x2-q*x1^2*x2^2
L10a22{1} 10 {1,-2,1,3,-2,3,3,-2,1,3} [[1, 1, -1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q*x1^2-q*x1^2*x2-q*x1^2*x2^2
L10a22{1} 10 {1,-2,1,3,-2,3,3,-2,1,3} [[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q*x1^2-q*x1^2*x2-q*x1^2*x2^2
L10a23{0} 10 {-1,2,-1,-1,-1,2,-1,-3,2,-3} [[1, -1, 1, -1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^-2*x2^2-q^-2*x1*x2^2-q^-2*x1^2*x2^2
L10a23{0} 10 {-1,2,-1,-1,-1,2,-1,-3,2,-3} [[-1, -1, 1, -1], [-1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1]] 1 -q^-2*x2^2-q^-2*x1*x2^2-q^-2*x1^2*x2^2
L10a23{1} 10 {-1,2,-1,-1,-1,2,-1,-3,2,-3} [[1, -1, 1, -1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]] 1 -q^-2*x2^2-q^-2*x1*x2^2-q^-2*x1^2*x2^2
L10a23{1} 10 {-1,2,-1,-1,-1,2,-1,-3,2,-3} [[-1, -1, 1, -1], [-1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^-2*x2^2-q^-2*x1*x2^2-q^-2*x1^2*x2^2
L10a25{1} 10 {1,-2,1,-2,3,3,-2,3,3,-2} [[1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -x1^2
L10a25{1} 10 {1,-2,1,-2,3,3,-2,3,3,-2} [[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -x1^2
L10a26{0} 13 {-2,3,-4,-2,-3,-1,2,-3,2,2,-3,-4,1} [[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, 1]] x1^(1/2)*x2^(1/2) -q^-1*x1^2*x2^-1
L10a26{0} 13 {-2,3,-4,-2,-3,-1,2,-3,2,2,-3,-4,1} [[-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, -1]] x1^(1/2)*x2^(1/2) -q^-1*x1^2*x2^-1
L10a26{1} 12 {-1,2,-1,3,2,2,-1,2,2,-3,2,2} [[1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q*x1^2
L10a26{1} 12 {-1,2,-1,3,2,2,-1,2,2,-3,2,2} [[-1, -1, 1, 1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1], [1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q*x1^2
L10a27{0} 10 {-1,2,2,-3,2,2,2,-1,2,-3} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q*x1^2-q*x1^2*x2-q*x1^2*x2^2
L10a27{0} 10 {-1,2,2,-3,2,2,2,-1,2,-3} [[-1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q*x1^2-q*x1^2*x2-q*x1^2*x2^2
L10a27{1} 10 {-1,2,2,-3,2,2,2,-1,2,-3} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q*x1^2-q*x1^2*x2-q*x1^2*x2^2
L10a27{1} 10 {-1,2,2,-3,2,2,2,-1,2,-3} [[-1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q*x1^2-q*x1^2*x2-q*x1^2*x2^2
L10a28{0} 10 {-1,-1,-1,2,2,-3,2,-1,2,-3} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-1*x1^2-q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a28{0} 10 {-1,-1,-1,2,2,-3,2,-1,2,-3} [[-1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-1*x1^2-q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a28{1} 10 {-1,-1,-1,2,2,-3,2,-1,2,-3} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-1*x1^2-q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a28{1} 10 {-1,-1,-1,2,2,-3,2,-1,2,-3} [[-1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-1*x1^2-q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a29{0} 10 {-1,-1,2,-1,2,-3,2,2,-3,2} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [-1, 1, -1, 1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a29{0} 10 {-1,-1,2,-1,2,-3,2,2,-3,2} [[-1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], [-1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -x1^2-x1^2*x2-x1^2*x2^2
L10a29{1} 10 {-1,-1,2,-1,2,-3,2,2,-3,2} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [-1, 1, -1, 1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a29{1} 10 {-1,-1,2,-1,2,-3,2,2,-3,2} [[-1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], [-1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -x1^2-x1^2*x2-x1^2*x2^2
L10a33{0} 13 {1,1,-2,-3,-3,4,1,-2,-3,-4,-4,3,1} [[1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, 1], [-1, -1, -1, -1, -1, -1, -1, -1]] x1^(1/2)*x2^(1/2) -x1^2*x2^-1
L10a33{0} 13 {1,1,-2,-3,-3,4,1,-2,-3,-4,-4,3,1} [[-1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1], [-1, -1, -1, -1, -1, -1, -1, -1]] x1^(1/2)*x2^(1/2) -x1^2*x2^-1
L10a33{1} 12 {-1,2,2,2,3,2,2,-1,2,2,-3,2} [[1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^2*x1^2
L10a33{1} 12 {-1,2,2,2,3,2,2,-1,2,2,-3,2} [[-1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -q^2*x1^2
L10a35{0} 10 {-1,-1,-1,-1,2,2,-1,-3,2,-3} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-2*x1^2-q^-2*x1^2*x2-q^-2*x1^2*x2^2
L10a35{0} 10 {-1,-1,-1,-1,2,2,-1,-3,2,-3} [[-1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-2*x1^2-q^-2*x1^2*x2-q^-2*x1^2*x2^2
L10a35{1} 10 {-1,-1,-1,-1,2,2,-1,-3,2,-3} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-2*x1^2-q^-2*x1^2*x2-q^-2*x1^2*x2^2
L10a35{1} 10 {-1,-1,-1,-1,2,2,-1,-3,2,-3} [[-1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-2*x1^2-q^-2*x1^2*x2-q^-2*x1^2*x2^2
L10a39{0} 12 {1,-2,-3,-2,-2,1,1,1,-2,3,-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)*x2^(1/2) -x2^2-x1*x2^2-x1^2*x2^2
L10a39{0} 12 {1,-2,-3,-2,-2,1,1,1,-2,3,-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 -x2^2-x1*x2^2-x1^2*x2^2
L10a39{1} 10 {-1,-1,2,2,-1,-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]] x1^(1/2)*x2^(1/2) -x1^2-x1^2*x2-x1^2*x2^2
L10a39{1} 10 {-1,-1,2,2,-1,-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 -x1^2-x1^2*x2-x1^2*x2^2
L10a4{0} 10 {-1,2,-1,2,-1,2,-3,2,-3,2} [[1, -1, 1, -1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -x2^2-x1*x2^2-x1^2*x2^2
L10a4{0} 10 {-1,2,-1,2,-1,2,-3,2,-3,2} [[-1, -1, 1, -1], [-1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -x2^2-x1*x2^2-x1^2*x2^2
L10a4{1} 10 {-1,2,-1,2,-1,2,-3,2,-3,2} [[1, -1, 1, -1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -x2^2-x1*x2^2-x1^2*x2^2
L10a4{1} 10 {-1,2,-1,2,-1,2,-3,2,-3,2} [[-1, -1, 1, -1], [-1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -x2^2-x1*x2^2-x1^2*x2^2
L10a43{0} 10 {1,-2,3,3,-2,1,-2,3,-2,1} [[1, 1, -1, 1, -1, 1, 1, 1, 1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -x1^2
L10a43{0} 10 {1,-2,3,3,-2,1,-2,3,-2,1} [[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [-1, 1, -1, 1]] x1^(1/2)*x2^(1/2) -x1^2
L10a44{0} 12 {1,1,1,1,-2,-3,-2,1,-2,3,-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*x1^2-2*q*x1^2*x2-q^2*x1^2*x2^2-3*q*x1^2*x2^2
L10a44{0} 12 {1,1,1,1,-2,-3,-2,1,-2,3,-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*x1^2-2*q*x1^2*x2-3*q*x1^2*x2^2
L10a46{0} 12 {1,1,-2,-3,-2,1,1,1,-2,3,-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*x1^2-2*q*x1^2*x2-q^2*x1^2*x2^2-3*q*x1^2*x2^2
L10a46{0} 12 {1,1,-2,-3,-2,1,1,1,-2,3,-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*x1^2-2*q*x1^2*x2-3*q*x1^2*x2^2
L10a49{0} 14 {-1,2,-1,-2,-3,-3,-3,-3,-2,-2,-1,2,3,-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, -1, -1]] x1^(1/2)*x2^(1/2) -q^-3*x1^-1*x2^2
L10a49{0} 14 {-1,2,-1,-2,-3,-3,-3,-3,-2,-2,-1,2,3,-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, -1, -1]] x1^(1/2)*x2^(1/2) -q^-3*x1^-1*x2^2
L10a49{1} 10 {-1,2,-3,-3,-3,2,-1,2,-3,2} [[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-1*x1^2
L10a49{1} 10 {-1,2,-3,-3,-3,2,-1,2,-3,2} [[-1, -1, 1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1], [1, -1, 1, -1]] x1^(1/2)*x2^(1/2) -q^-1*x1^2
L10a5{1} 10 {-1,2,-1,2,-1,-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]] x1^(1/2)*x2^(1/2) -x2^2-x1*x2^2-x1^2*x2^2
L10a5{1} 10 {-1,2,-1,2,-1,-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]] x1^(1/2)*x2^(1/2) -x2^2-x1*x2^2-x1^2*x2^2
L10a51{0} 10 {-1,2,-1,-1,-3,2,-3,2,-1,2} [[1, -1, 1, -1, 1, -1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]] 1 -q^-1*x1*x2^2-2*q^-1*x1^2*x2^2
L10a51{0} 10 {-1,2,-1,-1,-3,2,-3,2,-1,2} [[-1, -1, 1, -1, 1, -1], [-1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1]] 1 -q^-1*x1*x2^2-2*q^-1*x1^2*x2^2
L10a51{1} 10 {1,-2,1,3,-2,-2,3,-2,1,3} [[1, 1, -1, 1, -1, 1], [1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1]] 1 -x1*x2^2-2*x1^2*x2^2
L10a51{1} 10 {1,-2,1,3,-2,-2,3,-2,1,3} [[-1, 1, -1, 1, -1, 1], [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]] 1 -x1*x2^2-2*x1^2*x2^2
L10a52{0} 12 {1,-2,1,1,-2,3,-2,1,-2,1,-3,-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*x2^2-2*x1^2*x2^2
L10a52{0} 12 {1,-2,1,1,-2,3,-2,1,-2,1,-3,-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*x2^2-2*x1^2*x2^2
L10a53{0} 10 {1,-2,3,-2,1,-2,-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 -q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a53{0} 10 {1,-2,3,-2,1,-2,-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 -q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a54{1} 13 {-2,3,-4,-2,3,-2,3,1,2,-3,-4,2,-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, 1]] 1 -q^-1*x1^2-q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a54{1} 13 {-2,3,-4,-2,3,-2,3,1,2,-3,-4,2,-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, -1]] 1 q^-2*x2^2-q^-1*x1*x2-q^-1*x1*x2^2+4*q^-2*x1*x2^2-4*q^-1*x1^2*x2-2*x1^2*x2^2-3*q^-1*x1^2*x2^2+11*q^-2*x1^2*x2^2+q^-3*x1^2*x2^2
L10a54{1} 13 {-2,3,-4,-2,3,-2,3,1,2,-3,-4,2,-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, 1]] 1 -q^-1*x1^2-q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a54{1} 13 {-2,3,-4,-2,3,-2,3,1,2,-3,-4,2,-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, -1]] 1 q^-2*x2^2-q^-1*x1*x2-q^-1*x1*x2^2+4*q^-2*x1*x2^2-4*q^-1*x1^2*x2-2*x1^2*x2^2-3*q^-1*x1^2*x2^2+11*q^-2*x1^2*x2^2+q^-3*x1^2*x2^2
L10a55{0} 10 {1,-2,-2,-2,1,-2,1,3,-2,3} [[1, 1, -1, 1, -1, 1], [1, 1, 1, -1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1]] 1 -q^-1*x1*x2^2-q^-1*x1^2*x2^2
L10a55{0} 10 {1,-2,-2,-2,1,-2,1,3,-2,3} [[-1, 1, -1, 1, -1, 1], [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]] 1 -q^-1*x1*x2^2-q^-1*x1^2*x2^2
L10a56{0} 10 {-1,2,-1,-3,2,-3,2,-1,2,-3} [[1, -1, 1, -1, 1, -1], [-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1]] 1 -q^-1*x1*x2^2-2*q^-1*x1^2*x2^2
L10a56{0} 10 {-1,2,-1,-3,2,-3,2,-1,2,-3} [[-1, -1, 1, -1, 1, -1], [-1, -1, -1, 1, -1, 1, -1, -1, -1, 1, -1, 1, -1, 1]] 1 -q^-1*x1*x2^2-2*q^-1*x1^2*x2^2
L10a56{1} 10 {1,-2,1,3,-2,3,-2,1,-2,3} [[1, 1, -1, 1, -1, 1], [1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1]] 1 -x1*x2^2-2*x1^2*x2^2
L10a56{1} 10 {1,-2,1,3,-2,3,-2,1,-2,3} [[-1, 1, -1, 1, -1, 1], [1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1]] 1 -x1*x2^2-2*x1^2*x2^2
L10a57{0} 13 {2,-1,-2,-2,3,-4,-2,3,4,-2,3,4,-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, 1]] 1 x2^2-q^-1*x1*x2+3*x1*x2^2-2*q^-1*x1*x2^2-3*q^-1*x1^2*x2+q*x1^2*x2^2+5*x1^2*x2^2-7*q^-1*x1^2*x2^2+q^-2*x1^2*x2^2
L10a57{0} 13 {2,-1,-2,-2,3,-4,-2,3,4,-2,3,4,-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, -1]] 1 x2^2-q^-1*x1*x2+3*x1*x2^2-2*q^-1*x1*x2^2-3*q^-1*x1^2*x2+q*x1^2*x2^2+5*x1^2*x2^2-7*q^-1*x1^2*x2^2+q^-2*x1^2*x2^2
L10a57{0} 13 {2,-1,-2,-2,3,-4,-2,3,4,-2,3,4,-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, 1]] 1 -q^-1*x1^2-q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a57{0} 13 {2,-1,-2,-2,3,-4,-2,3,4,-2,3,4,-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, -1]] 1 -q^-1*x1^2-q^-1*x1^2*x2-q^-1*x1^2*x2^2
L10a57{1} 10 {1,-2,1,-2,3,-2,-2,3,3,3} [[1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1, 1, -1]] 1 -x1^2*x2-x1^2*x2^2
L10a57{1} 10 {1,-2,1,-2,3,-2,-2,3,3,3} [[-1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], [1, -1, 1, -1, 1, -1]] 1 -x1^2*x2-x1^2*x2^2
L10a59{0} 13 {-2,3,-2,-3,-3,4,-1,2,2,-3,4,2,1} [[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, 1]] 1 q*x2^2-x1*x2+3*q*x1*x2^2-2*x1*x2^2-3*x1^2*x2-q^2*x1^2*x2^2+5*q*x1^2*x2^2-5*x1^2*x2^2-q^-1*x1^2*x2^2
L10a59{0} 13 {-2,3,-2,-3,-3,4,-1,2,2,-3,4,2,1} [[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, 1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a59{0} 13 {-2,3,-2,-3,-3,4,-1,2,2,-3,4,2,1} [[-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, -1]] 1 q*x2^2-x1*x2+3*q*x1*x2^2-2*x1*x2^2-3*x1^2*x2-q^2*x1^2*x2^2+5*q*x1^2*x2^2-5*x1^2*x2^2-q^-1*x1^2*x2^2
L10a59{0} 13 {-2,3,-2,-3,-3,4,-1,2,2,-3,4,2,1} [[-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, -1]] 1 -x1^2-x1^2*x2-x1^2*x2^2
L10a59{1} 12 {-1,2,2,2,-3,2,-1,2,2,3,2,-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*x2^2-q*x1^2*x2^2
L10a59{1} 12 {-1,2,2,2,-3,2,-1,2,2,3,2,-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*x2^2-q*x1^2*x2^2

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

First page · Next 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.