Guoniu Han's Non-Anonymous Report on the article "The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal" by A. Baxter and D. Zeilberger

It is well-known that both the number of inversions and the major index is asymptotically normal. Here the authors proved that those two statistics are asymptotically joint-independently-normal. The method is very interesting, and is described in [Z] for the one dimension case. Notice that (inv, maj) is equidistributed to (maj, imaj) which is symmetry. See [Stanley, Enumerative Combinatorics, Vol. 2, formula (7.117)] for an explicit expression in term of hook length.

I certify that all formulas in the sections "A Combinatorial Interlude", "Back to inv-maj" and "Nice conjectures but what about proofs?" are correct. However I had some difficulties during my reading of the paper. It would be better if the authors provide more details.

1. Section "Guessing Polynomial Expressions for the Factorial Moments". The four conjectured expressions must have more leading terms, which will include all terms n^a*i^b such that a+b is maximal. The "degree" in (lower-degree-terms-in-(n,i)) must be the total degree. In the present form, we can't put i=n as required later in (Gnn').

2. Section "Nice conjectures but what about proofs?". Why a lower-order-term is necessary a lower-degree-term-in-(n,i) ? It seems not trivial, since a lower-order-term has the following form:
coeff(n) * FM(r',s')(n, i)

3. Page 6, line -6. Talking "leading terms of the FM's and the Mom's" means that FM and Mom are polynomials in n. It seems not trivial.

Some typos:

• FM[a1,...,ar] in page 6 and FM(r,s) in page 7. "()" or "[]" ?
• page 8, while the implication of Gnn is. Add "()" to Gnn
• page 9, La Grande Finale. "o" or "O" ?
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