Enumeration by associated reflections on Coxeter systems

We define a family of statistics over a generic finite Coxeter system indexed by subsets of its reflections set, and we study the corresponding generating functions, proving that they have a lot of interesting combinatorial properties. In particular, we prove equidistribution results, namely we investigate some conditions in order to have that different subsets have the same associated generating function. Furthermore, some previous results which hold for the symmetric group, are extended and generalized to any classical Weyl group.