The author proves five conjectures made by Kosa [1] and shows their usefulness in the automatic generation of  Sturmian  words. For a two-letter alphabet B, if p ( n ) denotes the number of factors of length n in an infinite word U, then U is Sturmian if p ( n ) = n + 1 for any n ∈ N. The best example of a Sturmian word is a Fibonacci word. Given a binary alphabet of the form A = { 0 , 1 }, the Sturmian words are generated by left and right endomorphisms of the form 1 → 01 and 1 → 10 respectively. The conjectures of Kosa deal with the completeness of such generating relationships.

The paper is highly theoretical and makes no mention of any application. The content of the paper does not appear to have immediate interest for many people. Among 16 references cited, only one other than the author’s directly addresses the problem.

The proofs are nicely stated and easy to follow. Instead of introducing all notation in the same place, however, the author sometimes introduces notation in the middle. This makes it difficult for the reader to find the meaning of certain symbols. I would have appreciated some more worked-out examples.

The formatting of the paper is nice, except for a few bad line breaks in the middle of equations. Overall, the paper is a nice exercise for a theoretician.