# $$\mathfrak{S}_n$$ is amazing (part 2)

See part 1 for the definition of $$\mathfrak{S}_n$$ and standard representation.

Let $$\mathbf{E}_n$$ denote the expected value of the number of cycles in the standard representation of permutation $$w \in \mathfrak{S}_n$$. What is the value of $$\lfloor \mathbf{E}_{1000} \rfloor$$?

×