Posted here Nov. 2, 2010

--------------------------- Aug 22 2010 10:05 am --------------------------- To: zeilberg@math.rutgers.edu 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 AMS (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 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. (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. (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