tailieunhanh - Báo cáo toán học: "How Berger, Felzenbaum and Fraenkel Revolutionized"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí toán học quốc tế đề tài: How Berger, Felzenbaum and Fraenkel Revolutionized. | How Berger Felzenbaum and Fraenkel Revolutionized COVERING SYSTEMS The Same Way that George Boole Revolutionized LOGIC Doron ZEILBERGER 1 leMori veRabi Aviezri Fraenkel who taught me that Games are Math and Math is a Game Abstract The Berger-Felzenbaum-Fraenkel approach to Covering Systems is exposited. In particular their gorgeous proof of the famous an an-1 theorem for exact covering systems found independently by Jamie Simpson is reviewed and the analogy of their approach to Boolean tautologies in Disjunctive Normal Form is pointed out. Preface There is more than one way to contribute to the preservation of the human species. The explicit way is to marry and have children and if your children turn out to be good you can and should feel proud. But a more efficient way is to be a matchmaker and make good matches and if the couples that you have introduced to each other turn out to have brilliant children then you may brag about them as though they were your own. This also applies to math. If you have introduced directly or indirectly Dr. Reuven to Professor Simeon and cast the deciding vote in the committee that admitted Mr. Levi to the . program then you are justffied in feeling enormous satisfaction when the Reuven-Simeon-Levi collaboration leads to a major breakthrough in a whole area of mathematics. If this collaboration also lead to a MOST BEAUTIFUL proof from the BOOK of BOOKS sought out for many years by the book s proposer and begged by him in hundreds of lectures then you can REALLY gloat. This happened to me with Reuven Marc Berger Simeon Aviezri Fraenkel Levi Alex Felzenbaum . The area that they revolutionized is covering systems and the beautiful proof that they found is the long-sought-for elementary proof of the Davenport-Rado-Mirsky-Newman an an-1 theorem. I will tell this story and the math later in this article. But let s start at the beginning. 1 Department of Mathematics Temple University Philadelphia PA 19122 USA. zeilberg@ .