Is there a general formula for the number of elements of order $k$ in $S_n$?
107010
How many elements of order $k$ are in $S_n$?
41294
Permutation module of $S_n$
152653
Count Eulerian cycles in $K_{n,2}$
46971
Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$
64118
Number of elements in a finite $\sigma$-algebra
61550
Existence of elements of order $p^k$ in a finite group
149609
Conditions on cycle types for permutations to generate $S_n$
8742
Examples and further results about the order of the product of two elements in a group
84491
Finding the smallest positive integer $n$ such that $S_n$ contains an element of order 60.
124224
How many groups of order $n$ with center {e} exist?
120095
How many ways to split n elements in k groups?
84132
Number of preimages of a group element under a homomorphism.
50762
If $S_n$ has cyclic subgroups of these orders or not?
19026
What do all the $k$-cycles in $S_n$ generate?
73224
number of ordered partitions of integer
26569
Counting binary operations on a set with $n$ elements
144821
Number of ordered pairs of subsets