Deriving Known Particular Solutions of the σ-Commutation Problem (σ ≠ 0, ±1) for a Toeplitz and a Hankel Matrix within a Unified Approach

In their preceding publication, the authors proposed a unified approach to the construction of matrix pairs \((T,H)\) that solve the \(\sigma \) -commutation problem for Toeplitz and Hankel matrices. Here, this approach is applied to the derivation of two classes of solutions that were earlier found by V.N. Chugunov from entirely different considerations.