How Berger, Felzenbaum, and Fraenkel Revolutionized COVERING SYSTEMS The Same Way that George Boole Revolutionized LOGIC

By Doron Zeilberger

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Written: April 7, 2000.

[Appeared in Elec. J. Combinatorics 8(2) (2001) (Special volume in honor of Aviezri Fraenkel), A1]

Dedicated to AVIEZRI FRAENKEL, on his 70th Birthday

Way back in the (early) eighties when I was in my (early) thirties, I have spent countless hours trying to find an elementary proof to the famous an=an-1 theorem about Covering Systems, begged by Erdos in many talks, all over the globe. I failed. Hence I could especially appreciate the BEAUTIFUL proof described in this article. I was so excited about this proof, that I described it, as a ten-minute digression, in many of my talks on unrelated subjects. Plus it was the center-piece of my talk in 1996, at the Tianjin Combinatorics meeting organized by Bill Chen. All these years I was hoping to write an expository paper about it, but never found the time. Luckily, Ed Scheinerman and Jamie Simpson asked me to contribute to the Fraenkel Festschrift that they are editing. So I finally decided that it is a great opportunity to finally realize my dream and at the same time pay homage to my great Rebbe, Aviezri Fraenkel.

P.S. This Birthday present is a bit late. Aviezri was born on June 7, 1929 (according to Who is Who in Israel)

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