Languages and the enumeration of planted plane trees

AbstractThis paper sets into relation three different classes of trees: (i) mod r-valent planted plane trees; (ii) r-valent planted plane trees; and (iii) subtrees of a certain infinite planted tree. Practically, all three classes of trees are counted by the same generating function, which is calculated by mapping trees on the words of a language. This leads to producing a one-to-one correspondence between the three classes by means of codes