A simple combinatorial proof of a generalization of a result of Polo

We provide a simple combinatorial proof of, and generalize, a theorem of Polo which asserts that for any polynomial $P\in \mathbb N[q]$such that $P(0)=1$ there exist two permutations $u$ and $v$ in a suitable symmetric group such that $P$ is equal to the Kazhdan-Lusztig polynomial $P^{v}_{u}$.