Ancestors graph and an upper bound for the subword complexity function (Q1935789)

General upper bounds for the subword complexity function of a fixed point of a primitive substitution have been proposed in the literature depending on the lengths of the images, under the substitution of the letters of the alphabet. In this very interesting paper, the author proposes another approach which is based on the ancestors graph of a substitution. He provides a characterization of the language of a fixed point of a substitution as the strongly connected components of the letters in its ancestors graph. His approach uses \(\mathbb Z\)-algebras of noncommutative polynomials over the alphabet of edges. This leads to an algorithm for the computation of an upper bound for the subword complexity. The author also raises a number of open questions.