In this survey, we study applications of combinatorial methods in the ring theory. Unlike the well-known survey by Ufnarovskii, we are more interested in the technique of obtaining these methods and not in the results themselves. Therefore, the theme of this survey is narrower and is more in correspondence with the authors' interests. The main subject here is the word combinatorial analysis and its applications, and also the notion of the canonical form of elements in different calculi.