TAILIEUCHUNG - Đề tài " Hypergraph regularity and the multidimensional Szemer´edi theorem "

We prove analogues for hypergraphs of Szemer´di’s regularity lemma and e the associated counting lemma for graphs. As an application, we give the first combinatorial proof of the multidimensional Szemer´di theorem of Furstenberg e and Katznelson, and the first proof that provides an explicit bound. Similar results with the same consequences have been obtained independently by Nagle, R¨dl, Schacht and Skokan. o 1. Introduction Szemer´di’s theorem states that, for every real number δ 0 and every e positive integer k, there exists a positive integer N such that every subset A of the set {1, 2, | Annals of Mathematics Hypergraph regularity and the multidimensional Szemer redi theorem By W. T. Gowers Annals of Mathematics 166 2007 897 946 Hypergraph regularity and the multidimensional Szemeredi theorem By W. T. Gowers Abstract We prove analogues for hypergraphs of Szemeredi s regularity lemma and the associated counting lemma for graphs. As an application we give the first combinatorial proof of the multidimensional Szemeredi theorem of Furstenberg and Katznelson and the first proof that provides an explicit bound. Similar results with the same consequences have been obtained independently by Nagle Rodl Schacht and Skokan. 1. Introduction Szemeredi s theorem states that for every real number Ỗ 0 and every positive integer k there exists a positive integer N such that every subset A of the set 1 2 . N of size at least ỖN contains an arithmetic progression of length k. There are now three substantially different proofs of the theorem Szemeredi s original combinatorial argument Sz1 an ergodic-theory proof due to Furstenberg see for example FKO and a proof by the author using Fourier analysis G1 . Interestingly there has for some years been a highly promising programme for yet another proof of the theorem pioneered by Vojta Rodl see for example R developing an argument of Ruzsa and Szemeredi RS that proves the result for progressions of length three. Let us briefly sketch their argument. The first step is the famous regularity lemma of Szemeredi Sz2 . If G is a graph and A and B are sets of vertices in V then let e A B stand for the number of pairs x y E A X B such that xy is an edge of G. Then the density d A B of the pair A B is e A B A B . The pair is e-regular if Id A B d A B l e for all subsets A c A and B c B such that A e A and B e B . The basic idea is that a pair is regular with density d if it resembles a random graph with edge-probability d. Very roughly the regularity lemma asserts that every graph can be decomposed into a few pieces almost all of .

• Thạc sĩ - Tiến sĩ - Cao học
• Hypergraph regularity
• subjects of mathematics
• science reports
• studied mathematics
• natural sciences
• scientific research
• Research methods
• Data collection methods
• Understanding scientific research
• Ensuring research validity
• Measurement techniques
• Sampling methods
• Scientific research capacity
• Educational institutions
• Policy and management studies
• Vietnam Academy for Ethnic minorities
• Scientific bases
• earth sciences
• Research
• VNU Journal of Science
• scientific reports
• Action research
• linguistics
• research projects
• Foreign Languages
• cooperative research
• Renewable energy
• Introduction to research
• Scientific investigation
• Scientific investigation research
• Experimental designs
• Measurement of variables
• Reading research
• Conducting and reading research
• Research process
• Research report
• Purpose of research
• Scientific method
• Conducting research
• The effect of university autonomy on training and scientific research
• Vietnam national university of agriculture
• Training and scientific research
• Vascular plant
• Flora
• Yen Tu
• Quang Ninh Research Forest
• statements and documents scientific reports
• medical reports
• medical knowledge
• medical research
• clinical trials
• medical management
• health care
• Methods in behavioral research
• Behavioral research
• Scientific understanding
• Fundamental research issues
• Measurement concepts
• Observational methods
• reading comprehension
• education
• optimal picket
• model creation
• urban expansion
• organizing spatial
• Journal of Science
• Journal of Technology
• Technology Management
• Research quality
• Strategy and policy
• Summary of Doctoral thesis
• Summary of Doctoral thesis in public Management
• State management
• Female scientific research human
• Research human resource development
• Scientific research and teaching
• Defense and security education
• Current situation and solutions
• Security education
• Structural biochemistry
• epigenetics
• MicroRNAs
• Tạp chí khoa học
• Tạp chí Công nghệ
• Quản lý công nghệ
• Human resources
• Science management
• Poliomyelitis vaccine Research
• Non Ri Maprec
• Production center