Eulerian calculus, II: An extension of Hanʹs fundamental transformation

In our first Eulerian Calculus paper, we introduced the k-descent and k-excedance statistics on words, considered various bijections associated with them and calculated their distributions. In this paper we consider the k-major and k-den statistics and show that the joint des-maj and exc-den distributions of that k-extension are identical. We also consider the generating functions for these statistics.