On the trace map for products of matrices associated with substitutive sequences (Q1182244)

Studying the discrete Schrödinger operator, or equivalently the mass and spring problem, leads to the study of the trace of a product of \(2\times 2\) transfer matrices. In the case where these matrices take only two vlaues and are generated by a substitution, a formula for computing the trace of products has been given by the author and the reviewer [C. R. Acad. Sci., Paris, Sér. II 302, 1135-1136 (1986; Zbl 0587.65033)]. This result has been studied in more details by other authors [\textit{M. Kolář} and \textit{M. K. Ali}, Phys. Rev. A 42, 7112-7124 (1990); \textit{M. Kolář} and \textit{F. Nori}, Phys. Rev. B 42, 1062-1065 (1990); and further developments are given by the author and Wen]. In the paper under review the author proves a universal divisibility property for trace- polynomials which has been conjectured by Kolář and Ali.