Recursive Statistics on Words

A general machine for constructing a large class of statistics on words will be desribed. These statistics, which have a certain recursive structure, are called {\it splittable}. The classical Mahonian statistics major index (maj) and inversion number (inv) are examples, as are more modern Mahonian statistics such as the "Z" statistic of Zeilberger and Bressoud, Denert's "den" and Rawlings' interpolating statistic, "r-maj". I will explain how, and in what sense, the entire class of splittable Mahonian statistics is generated by the single statistic "inv". I will also describe other non-Mahonian statistics which have a similar recursive structure and conclude with some remarks about the extension of these ideas to other combinatorial objects.