Enumeration of several combinatorial statistics in $AAA_n$ surprisingly gives clean results. In this talk, we cover two such statistics, excedance and descent-length. Apart from getting clear answers, we are also able to get the mean and sometimes Central Limit Theorems for the random variable that takes these statistics as values when permutations are sampled from $AAA_n$.
Extensions to type B and type D Coxeter groups are given whenever applicable. Proofs seem to make use of various techniques and are many times of independent interest.
