Recursive statistics on words

Abstract

We describe a general machine for constructing statistics on words with a certain recursive structure. The classical Mahonian statistics, major index and inversion number, are examples, as are more modern Mahonian statistics, including those of Zeilberger and Bressoud, Denert, Han, Rawlings and Kadell. We give simple recursive procedures for calculating these statistics, as well as statistic-preserving bijections among them. We also describe other non-Mahonian distributions with similar recursive structures.