Question

Let q $q$ be a power of a prime. It's well-known that the function B(n, $B(n, q) = 1/n sum_{d \frac{1}{n} \sum_{d | n} \mu(n/d) q^d is mu \left( \frac{n}{d} \right) q^d$ counts both the number of irreducible polynomials of degree n $n$ over Fq$\mathbb{F}_q$ and the number of Lyndon words of length n $n$ over an alphabet of size q. $q$. Does there exist an explicit bijection between the two sets?}