CWR sequence of invariants of alternating links and its properties

Michal Jablonowski

Published 2024-06-07Version 1

We present the $CWR$ invariant, a new invariant for alternating links, which builds upon and generalizes the $WRP$ invariant. The $CWR$ invariant is an array of two-variable polynomials that provides a stronger invariant compared to the $WRP$ invariant. We compare the strength of our invariant with the classical HOMFLYPT, Kauffman $3$-variable, and Kauffman $2$-variable polynomials on specific knot examples. Additionally, we derive general recursive "skein" relations, and also specific formulas for the initial components of the $CWR$ invariant ($CWR_2$ and $CWR_3$) using weighted adjacency matrices of modified Tait graphs.