Can I read On the Cardinality of a Factor Set in the Symmetric Group on EtoBox?

On the Cardinality of a Factor Set in the Symmetric Group by Yordzhev, Krasimir is a scholarly article available to read on EtoBox.

What is On the Cardinality of a Factor Set in the Symmetric Group about?

Let $n$ be a positive integer, $\sigma$ be an element of the symmetric group $\mathcal{S}_n$ and let $\sigma$ be a cycle of length $n$. The elements $\alpha ,\beta \in \mathcal{S}_n$ are $\sigma$-equivalent, if there are natural numbers $k$ and $l$, such that $\sigma^k \alpha =\beta\sigma^l$, which is the same as the condition to exist natural numbers $k_1$ and $l_1$, such that $\alpha = \sigma^{k_1} \beta\sigma^{l_1}$. In this work we examine some properties of the so defined equivalence relation. We build a finite oriented graph $\Gamma_n$ 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.

Author

Yordzhev, Krasimir

Published

2014

Language

EN