Read e-book online An Irregular Mind: Szemerédi is 70 PDF

By Noga Alon (auth.), Imre Bárány, József Solymosi, Gábor Sági (eds.)

ISBN-10: 3642144438

ISBN-13: 9783642144431

Szemerédi's effect on modern arithmetic, specially in combinatorics, additive quantity thought, and theoretical computing device technological know-how, is big. This quantity is a party of Szemerédi's achievements and character, at the celebration of his 70th birthday. It exemplifies his remarkable imaginative and prescient and detailed state of mind. a couple of colleagues and associates, all most sensible specialists of their fields, have contributed their newest examine papers to this quantity. the subjects contain extension and purposes of the regularity lemma, the life of k-term mathematics progressions in numerous subsets of the integers, extremal difficulties in hypergraphs thought, and random graphs, them all attractive, Szemerédi sort arithmetic. It additionally comprises released money owed of the 1st , very unique and hugely winning Polymath initiatives, one led by way of Tim Gowers and the opposite via Terry Tao.

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Graham and J . Spencer, On graphs which contain all sparse graphs, Ann. , 12 (1982), 21-26. [12J S. N. Bhatt, F . Chung , F. T . Leighton and A. Rosenberg, Universal graphs for bounded-degree trees and planar graphs, SIAM J. Disc . , 2 (1989), 145-155 . [13J S. N. Bhatt and C. E. Leiserson, How to assemble tree machines, in: Advances in Computing Research, F. , 1984. [14J S. Butler, Induced-universal graphs for graphs with bounded maximum degree, Graphs and Combinatorics, 25 (2009), 461-468 . [15J M.

Notice that about 1/4 of the arithmetic progressions in 1,2,3, .. , N has an even starting point and an even gap, and these arithmetic progressions, consisting of even integers only, do not even intersect our large set S of density 1/2. 1(a). 1(a) as follows (we lose a logarithmic factor). 2. Let S be an arbitrary subset of the discrete interval {I, 2, ... , N}, and let T 2: 1000 be an arbitrary integer with N > 100T2 . 28) ~ ~ ('~I - ~. 1)' < clTlogT, n=T (mod m) where Cl is an absolute constant (say, Cl = 400 is a good choice).

In other words, the problem of the distribution of a billird path in the unit square is equivalent to the distribution of the corresponding torus-line in the 2 x 2 square. As far as I know, the first appearance of the geometric trick of unfolding is in a paper of D. Konig and A. Szucs from 1913, and it became widely known after Hardy and Wright included it in their famous book on number theory. Konig and Sziics used the trick of unfolding (combined with the Kronecker-Weyl theorem) to prove the following elegant property of the billiard path in a square.

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An Irregular Mind: Szemerédi is 70 by Noga Alon (auth.), Imre Bárány, József Solymosi, Gábor Sági (eds.)


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