Written: June 4, 2023.
Richard Stanley famously proved that Young's Lattice, L(m,n) (the integer partitions with at most m parts with largest part at most n under the natural ordering), has the Sperner property, by proving (indirectly) that there EXISTS a "central chain decomposition", but left open even the existence of a symmetric chain decomposition.
Bernt Lindstrom found a nice explicit construction for L(3,n), shortly followed by a nice, quite a bit more complicated construction, by Doug West for L(4,n), both published in the first volume of the European Journal of Combinatorics. Many people (including, yours truly), tried, in vain, to find an analogous explicit construction for L(5,n). So this major challenge was wide open for 43 years!
When my former PhD student, Xiangdong Wen, sent me his breakthrough, I was so excited. It was an ingenious computer-assisted explicit construction, with a beautiful ingenious, very insightful, symbolic-computational proof of its correctness. But, "insightful" or not, the very fact that it exists is very interesting and very significant. The facts:
275 + 845 + 1105 + 1335 = 1445 , and
958004 + 2175194 + 4145604 = 4224814 ,
even if they do not add any "number-theoretical insight", (today they are purely routine to verify) are much more interesting and significant, than anything the learned referee ever did.
(see his (or her) unfair snotty report.)
Of course, the most important place is the arxiv, but it is still nice to have it published in a peer-reviewed journal. Xiangdong asked me to recommend a journal. I strongly believe that such a major breakthrough, in an ideal world, should go to the Annals of Mathematics, or any of the so-called "top-tier journals". Since I know the abstract-snobbism of the current mathematical "mainstream", and since Xiangdong works for Wolfram, and does not need a "prestigious" journal for his advancement, and since the two predecessors, by Lindstrom and West, were published in the good old days in the European Journal of Combinatorics, I stupidly recommended that he submit it there. Little did I know that the obsession with so called "insight" (which is a euphemism for "fancy high-brow" math) has gone too far.
I also found two errors (in addition to the erroneous rejection, of course) in the inhuman rejection slip signed by the Editor in Chief, Patrice Ossona de Mendez, and Vice-Editor in Chief, Marthe Bonamy. First, Xiangdong Wen is obviously not a Professor, since he works for Wolfram, he is "only" a Dr., so the form letter should have been edited to start with
"Dear Dr. Wen,"
More important, I strongly disagree with the sentence:
"We are sorry to inform you that a referee has advised against publication, and that we must therefore reject it."
As editors, you are not "forced" to follow the referee's "advice". I hope that you have a mind of your own. So the rejection slip, more honestly, should say:
"We are sorry to inform you that a referee has advised against publication, and that we concur with his (or her) decision."
This way you should be accountable for this very unfair and erroneous rejection.
I also strongly recommend to the editorial board of EJC to resign from a journal that can make such a grave editorial blunder.