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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 them defied
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: