On embeddings of shifts of finite type into the golden-mean-Dyck shift

We consider the embedding problem for shifts of finite type into the golden-mean-Dyck shift. To this end, we study periodic points in the golden-mean-Dyck shift. We obtain the number of such periodic points of length n in the form of the trace of the n-th term of a sequence of the associated matrices. In view of this result, we also give simple examples of embeddings of shifts of finite type into the golden-mean-Dyck shift. Additionally, we generalize this result to the Markov-Dyck shift.