The Narrow-Minded and Human-Supremacist Referee's Report [and Zeilberger's Response] of the article" The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal" (by Andrew Baxter and Doron Zeilberger) that was rejected by Proceedings of the American Mathematical Society

Posted Oct. 5, 2010

The journal Proceedings of the American Mathematical Society, erroneously (and, of course, stupidly) rejected Andrew Baxter and Doron Zeilberger's article The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal, based on a referee report that clearly showed that he or she do not know how to read and understand a computer-assisted proof. It is also clear that the referee thinks that a mathematically rigorous article has to be written in the usual boring style. "Excited and chatty" does not mean non-rigorous.

Here is the report and Doron Zeilberger's responses.

Referee's report:

>(1) Summary:
>This paper outlines a method of proving that the pair permutation statistics
>(inv,maj) are asymptotically joint-independently-normal. At the heart of this
>is an interesting fast algorithm for computing the generating function for
>the pair (inv,maj). The paper is written in a chatty and excited style, but is
>painful to read since there are many missing details. I would very much like
>to see this result proved in a conventional style.

This article is written in a very clear and lucid way, outlining all the ideas.
It also describes where to find the corroborating computer software and its
output that validate the arguments. This part has no place in the body
of the article, and is described in the accompanying webpage,
where all the claims are documented.

>(2) Decision:
>I do not recommend this paper for publication for the following reasons:
>(i) The paper only gives an overview of the method of proof, so I cannot
>vouch for its correctness.

A slight effort to examine the accompanying Maple package,
and the above webpage, should have convinced any Maple-literate person of
the validity of the arguments. If the referee is not familiar with Maple, then
he or she should have refused to review this paper.

>(ii) Far too many aspects of this purported proof are essentially left as
>"exercises to the reader".

Everything is spelled-out, and I have no idea what the referee is talking about.
Unlike the conventional boring style of mathematical discourse, it presents the
ideas very clearly.

The associate editor who handled the submission agreed with the referee stating:

"Under its current policy, PAMS accepts papers that present mathematics supported by proofs that meet traditionally accepted rigorous standards."

As I said in Opinion 112, the present computer-assisted proof is far more rigorous than most human-generated proofs in the PAMS (or any other mathematics periodical, for that matter).

Added Oct. 27, 2010: This is not the first bad decision of the PAMS. About a year ago another associate editor rejected (without a referee report, i.e. solely based on an editorial decision, unless you count him as a referee) a beautiful article. When I inquired, he replied:
Hi Doron,
It probably was a bad decision.  The essential problem I have as PAMS editor
is that we have a rough quota of accepting 1 in 4 articles, and a lot of
good submittals.  I often get frustrated at dealing with so many articles
and reject some of them for rather vacuous reasons.  And, under this system,
authors without a proven track record and/or who don't solve a known problem
are at a disadvantage.  So, the rejection is more a reflection of these
conditions than a judgement about the math.


[Name removed]

Added Nov. 6, 2010: Watch the lecture .
Andrew Baxter and Doron Zeilberger's Article

Opinion 112 of Doron Zeilberger