Alguns problemas mais elaborados em análise combinatória elementar, II: Combinatória de palavras
Year: 2026
Type: article
Abstract: In the study of elementary combinatorial analysis, the principles of addition and multiplication are introduced, as well as their applications to solving counting problems involving permutations and combinations with or without repetition. However, students frequently pose variations of these problems in class which are often not addressed in widely used textbooks or undergraduate programs. In this article, which corresponds to the second part of a two-part exposition, we examine some problems involving word counting and restricted multisets using the inclusion-exclusion principle and generating functions. Motivated by the introduction of generating functions in the solution of the problems, we offer a brief review of the main concepts related to these functions, highlighting aspects that we call classic and modern. We conclude the article by mentioning some topics of potential interest for further study of combinatorial analysis at a relatively elementary level.
Author: José Ricardo Gonçalves Mendonça
Institution: Universidade de São Paulo
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7225409052