CWR sequence of invariants of alternating links and its properties

We present the [Formula: see text] invariant, a new invariant for alternating links, which builds upon and generalizes the [Formula: see text] invariant. The [Formula: see text] invariant is an array of two-variable polynomials that provides a stronger invariant compared to the [Formula: see text] invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman [Formula: see text]-variable, and Kauffman [Formula: see text]-variable polynomials on specific knot examples. Additionally, we derive general recursive “skein” relations, and also specific formulas for the initial components of the [Formula: see text] invariant using weighted adjacency matrices of modified Tait graphs.