Permutation of $n$ elements is a bijection from $\{1,2,...,n\}$ to itself. We denote by $\left( \begin{smallmatrix} i_1&i_2&...&i_n \\ j_1&j_2&...&j_n \end{smallmatrix} \right)$, where $i_1,\,i_2,... ,\,i_n$ are different elements of the set $\{1,2,... ,n\}$ and $j_1,\,j_2,... ,\,j_n$ are different elements of the set $\{1,2,... ,n\}$, permutation $a$ such that $a(i_k)=j_k$ for all $k\in \{1,2,... ,n\}$. We can graph a permutation in the following way. On a plane, draw elements of the set $\{1, 2, ..., n\}$, then for each element $i$ graph an arrow from $i$ to $a(i)$. The resulting graph is called the graph of the permutation. The set of permutations of $n$ elements is denoted by $S_n$.