Abstract
Let n be a positive integer, σ be an element of the symmetric group [Formula: see text] and let σ be a cycle of length n. The elements [Formula: see text] are σ-equivalent, if there are natural numbers k and l, such that σk α = βσl, which is the same as the condition to exist natural numbers k1 and l1, such that α = σk1 βσl1. In this work, we examine some properties of the so-defined equivalence relation. We build a finite oriented graph Γn with the help of which is described an algorithm for solving the combinatorial problem for finding the number of equivalence classes according to this relation.
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