A Recursive Formulation of Sylvester's Bijection Between Odd and Distinct Partitions

By Doron Zeilberger

Written: ca. 1984 .
Published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger: Jan. 3, 2011.
This gem, even though it is not dated, must have been written in 1984. In 1983, I still used typists, and by 1985 I used Troff. This article was typeset with a primitive word processor and was printed on a dot-matrix printer. It is one of my favorites, and of course was stupidly rejected, by two stupid journals and by two stupid referees. But now we have the internet, and the broad-minded editors of the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger kindly agreed to accept it without refereeing.

The first stupid journal to reject it was the pretentious "American Journal of Mathematics". I naively believed that since the Journal owes its existence to James Joseph Sylvester, and this paper is a nice approach to his bijection published there, there would be happy to publish it. Boy, was I naive. They would probably reject all Sylvester's papers if he would have been alive in 1984. They didn't even send the paper to referees. The editor (I believe it was J.-I. Igucha) wrote me a very condescending letter that was intended to be "nice", saying that they "don't publish papers on material that they don't understand". Hello, Prof. Igucha (and Prof. Ono et. al.), if you don't understand what Sylvester did, you should resign! I told my good friend James Joseph Sylvester, and he got very mad, and wrote them a nasty letter from Heavens, (communicated by me), that they never replied to. Shame on you Prof. Igucha and the rest of the "high-brow", snotty editorial board of the Amer. J. of Mathematics in 1984.

The second stupid journal that rejected it was the unpretentious, low-brow, yet apparentaly also stupid Ars Combinatorica. The referee just missed the point.

But yea for the internet! I just scanned this gem and am hereby publishing it in this very high-quality, yet unpretentious, electronic journal. History will decide whether this unpretentious paper is "important" or not, and even if it is not, it was fun to write.

Personal Journal of Shalosh B. Ekhad and Doron Zeilberger

Homepage of Doron Zeilberger