Uma fórmula para o número de permutações circulares com repetição via ações de grupos

Abstract

In the Combinatorics studied in high school and in the early stages of college, a lot of emphasis is given to permutations. Linear permutations with either distinct or repeated elements are treated, as well as circular permutations with distinct elements, but nothing is mentioned regarding circular permutations with repeated elements. The goal of this work is to provide a reference in Portuguese for a formula that can be used in this problem, accompanied by its demonstration, which relies on the Theory of Group Actions and Burnside’s Theorem. These topics are also briefly treated in this paper for completeness purposes.