By Dominique Foata and Doron Zeilberger
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Appeared in Advances in Applied Math v. 27 (2001) 390-404 [FoataFest issue]

Copyright(c)2001 by Academic Press (available from IDEAL).

Written: Oct. 31, 2000.

The Second Author Dedicates His Part To The First Author, on his 65th Birthday

Eric Babson and Einar 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 our four turned out to be easy grit to 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 the ingenious combinatorial savoir-faire of the human Dominique Foata.

Note: The human Dennis White independently proved the first two conjectures.

IMPORTANT: This article is accompanied by a Maple package PERCY , that also requires the Maple package ROTA. Here is the input file for PERCY, that would produce by doing: " maple -q < inPERCY > outPERCY " the output file for PERCY.

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