Burnside's lemma for counting orbits in M x N matrix
8627
Number of equivalence classes of $w \times h$ matrices under switching rows and columns
75461
If $n>m$, then the number of $m$-cycles in $S_n$ is given by $\frac{n(n-1)(n-2)\cdots(n-m+1)}{m}$.
72326
Determinant of block matrix with commuting blocks
40566
Counting surjective functions
60005
Determining the Orbits/Orbit Space of $O(3)$ on Real 3 by 3 Traceless Symmetric Matrices
125889
Determinant of rank-one perturbations of (invertible) matrices
57221
counting the number of elements in a conjugacy class of $S_n$
12955
Classification of $n\times n$ real matrices up to congruence
64168
Problem 4.6, I. Martin Isaacs' Character Theory
138178
Proving the number of iterations in the Euclidean algorithm
46971
Number of surjections from $\{1,...,m\}$ to $\{1,...,n\}$
13822
Expected number of hamiltonian paths in a tournament
78298
On the nilpotence of the matrix $AB-BA$
28468
Haar measure on $SO(n)$
147746
Characterisation of the squares of the symmetric group
89553
proof that every finite matrix has an annihilating polynomial
15202
the root of $N$th transpose matrix