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An Irregular Mind

Part of the Bolyai Society Mathematical Studies Book Series (volume 21)

Editors: Bárány, Imre; Solymosi, József; Sági, Gábor

DOI: 10.1007/978-3-642-14444-8

ISBN: 978-3-642-14443-1

Publisher: Springer Berlin Heidelberg - Springer Journals

Jan 31, 2010

1 - 10 of 23 Chapters

Available

Universality, Tolerance, Chaos and Order

Alon, Noga

Pages: 21 –37

[What is the minimum possible number of edges in a graph that contains a copy of every graph on n vertices with maximum degree a most k ? This question, as well as several related variants, received a considerable amount of attention during the last decade. In this short survey we describe the...
Available

Super-Uniformity of The Typical Billiard Path

Beck, József

Pages: 39 –129

[1. Introduction. Uniform distribution—also called equidistribution—is a truly fundamental concept. The famous Weyl’s Criterion (about uniform distribution) is perhaps the most frequently quoted result in whole mathematics. This volume celebrates the 70th birthday of Endre Szemerédi: the famous...
Available

Percolation on Self-Dual Polygon Configurations

Bollobás, Béla; Riordan, Oliver

Pages: 131 –217

[Recently, Scullard and Ziff noticed that a broad class of planar percolation models are self-dual under a simple condition that, in a parametrized version of such a model, reduces to a single equation. They state that the solution of the resulting equation gives the critical point. However, just...
Available

On Exponential Sums in Finite Fields

Bourgain, Jean

Pages: 219 –242

[The purpose of this paper is to establish certain multilinear exponential sums in arbitrary finite fields, extending some of the results from [1] for prime fields.]
Available

An Estimate of Incomplete Mixed Character Sums

Chang, Mei-Chu

Pages: 243 –250

[Dedicated to Endre Szemerédi for his 70th birthday. In this note we consider incomplete mixed character sums over a finite field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}...
Available

Crossings Between Curves With Many Tangencies

Fox, Jacob; Frati, Fabrizio; Pacht, János; Pinchasi, Rom

Pages: 251 –260

[Let A and B be two families of two-way infinite x-monotone curves, no three of which pass through the same point. Assume that every curve in A lies above every curve in B and that there are m pairs of curves, one from A and the other from 13, that are tangent to each other. Then the number of...
Available

An Arithmetic Regularity Lemma, An Associated Counting Lemma, and Applications

Green, Ben; Tao, Terence

Pages: 261 –334

[To Endre Szemerédi on the occasion of his 70th birthday Szemerédi’s regularity lemma can be viewed as a rough structure theorem for arbitrary dense graphs, decomposing such graphs into a structured piece, a small error, and a uniform piece. We establish an arithmetic regularity lemma that...
Available

Yet Another Proof Of Szemerédi's Theorem

Green, Ben; Tao, Terence

Pages: 335 –342

[To Endre Szemerédi on the occasion of his 70th birthday Using the density-increment strategy of Roth and Gowers, we derive Szemerédi’s theorem on arithmetic progressions from the inverse conjectures GI (s) for the Gowers norms, recently established by the authors and Ziegler in [8].]
Available

Online Linear Discrepancy of Partially Ordered Sets

Keller, Mitchel T.; Streib, Noah; Trotter, William T.

Pages: 343 –357

[This article is dedicated to Professor Endre Szemerédi on the occasion of his 70th birthday. Among his many remarkable contributions to combinatorial mathematics and theoretical computer science is a jewel for online problems for partially ordered sets: the fact that h(h + l)/2 antichains are...
Available

On The Triangle Removal Lemma For Subgraphs of Sparse Pseudorandom Graphs

Kohayakawa, Yoshiharu; RÖdlt, VojtĚch; Schacht, Mathias; Skokan, Jozef

Pages: 359 –404

[We study an extension of the triangle removal lemma of Ruzsa and Szemeredi [Triple systems with no six points carrying three triangles, Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II, North-Holland, Amsterdam, 1978, pp. 939-945], which gave rise to a purely combinatorial...

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