Proceedings of the American Mathematical Society's rejection message of the article "The Number of Inversions and the Major Index of Permutations are Asymptotically Joint-Independently Normal" (by Andrew Baxter and Doron Zeilberger)

Posted here Nov. 2, 2010

Aug 22 2010 10:05 am
Cc: Email removed
From: "On behalf of [Name Removed]" 
Subject: PROC 100407-Zeilberger - Decision

This message is from the AMS Peer Review system on behalf of  [Name removed]
PLEASE DO NOT REPLY TO THIS EMAIL. Kindly forward all correspondence to 
[name removed]

Dear Doron,

I have had one referee review your paper

   The Number of Inversions and the Major Index of Permutations are
Asymptotically Joint-Independently Normal
   by Andrew Baxter
      Doron Zeilberger

thoroughly and sent it to a second colleague for further feedback.
As I would have expected, it is very entertaining.  It also poses
serious problems as a submission to the Proceedings.  Under its
current policy, PAMS accepts papers that present mathematics supported
by proofs that meet traditionally accepted rigorous standards.

I concur with the referee that your manuscript outlines arguments,
leaving details of proof to the reader.  While I can anticipate your
reaction that the core of the paper consists of an algorithm and computation,
the issue is not the nature of the paper but rather that the arguments and
the code need more explanation in print.  You might want to look at the
article "The complete generating function for Gessel walks is algebraic"
by Bostan and Kauers, in the most recent edition of the Proceedings of the
(September 2010) as a model for a paper that marries the best of
conventional presentation and the excitement of experimental mathematics.

I am sorry that I cannot accept the manuscript as it stands.  If you wish
to rewrite it so that it takes a more scholarly tack with enough detail for
the careful reader to reconstruct the main results -- and it remains under
fifteen pages -- I will be happy to submit it to a new referee.  On the other
hand, you may wish instead to send a revised paper to Jim Haglund who handled
the example I alluded to.

Best regards,

[Name Removed]
Editor, Quantized enveloping algebras and Lie algebras
Proceedings of the American Mathematical Society

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
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.

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

(3) Typos/comments for the authors:
Page 1. The result of this paper is claimed as a longstanding conjecture.
To whom is it attributed?
Page 2 lines 3/4. "seminal lovely".
Page 2 line -2. "!."
Page 3 second last paragraph. "brute-brute-force" should be "brute force".
Page 3 last paragraph "brute-force" should be "brute force".
Page 6 line -7 "put-up with" should be "put up with".
Page 8 line 6 "all we need (do) is (to) verify".
Page 9 equations "FM(2,0)(n,i) = " and "\alpha(2r,2s)(n)=" are missing
commas after them (in order to be consistent).
Page 10: "Tilde" should be "$\sim$".
Page 10: "Oren Patashnik" and "Donald E. Knuth" should be swapped.

Andrew Baxter and Doron Zeilberger's Article

Opinion 112 of Doron Zeilberger