Advances in Appl. Math., 27, 2001, p. 390-404.

Dominique Foata and Doron Zeilberger

Babson-Steingrímsson Statistics Are Indeed Mahonian (and Sometimes Even Euler-Mahonian)

Abstract. Eric Babson and Einer Steingrimsson discovered, using their ingenuity and their computer, a bunch of new permutation statistics, that appeared to be Mahonian. Some of these they can do, but eight of uhem debied them. Here we prove the Mahonity of four of them, generously leaving the other four to other people (maybe you!). Three of of our four turned out to be easy grit to the DZ's "Umbral Transfer Matrix Method" mill (that is based on Gian-Carlo Rota's seminal notion of the umbra). But the other one needed an adequate combinatorial construction.

IMPORTANT: This article is accompanied by a Maple package PERCY , that also requires the Maple package ROTA.

All those packages can be retrieved from Doron Zeilberger's home page.

foata@math.u-strasbg.fr, zeilberg@math.temple.edu

The following versions are available: