The Kauffman X-polynomial, also called the normalized bracket polynomial, is a 1-variable knot polynomial denoted X, ℒ, or F, and defined for a link L by X_L(A) congruent (-A^3)^(-w(L)) 〈L〉(A), where 〈L〉 is the bracket polynomial and w(L) is the writhe of L. It is implemented in the Wolfram Language as KnotData[knot, BracketPolynomial]. This polynomial is invariant under ambient isotopy, and relates mirror images by X_L^* = X L_L(A^(-1)).

bracket polynomial | Jones polynomial | Kauffman polynomial F | knot invariant | knot polynomial

KnotData