Relevant bibliographies by topics / Szemerédi

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Szemerédi'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Szemerédi"

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ZHAO, YUFEI. "An arithmetic transference proof of a relative Szemerédi theorem." Mathematical Proceedings of the Cambridge Philosophical Society 156, no. 2 (November 14, 2013): 255–61. http://dx.doi.org/10.1017/s0305004113000662.

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AbstractRecently, Conlon, Fox and the author gave a new proof of a relative Szemerédi theorem, which was the main novel ingredient in the proof of the celebrated Green–Tao theorem that the primes contain arbitrarily long arithmetic progressions. Roughly speaking, a relative Szemerédi theorem says that if S is a set of integers satisfying certain conditions, and A is a subset of S with positive relative density, then A contains long arithmetic progressions, and our recent results show that S only needs to satisfy a so-called linear forms condition.This paper contains an alternative proof of the new relative Szemerédi theorem, where we directly transfer Szemerédi's theorem, instead of going through the hypergraph removal lemma. This approach provides a somewhat more direct route to establishing the result, and it gives better quantitative bounds.The proof has three main ingredients: (1) a transference principle/dense model theorem of Green–Tao and Tao–Ziegler (with simplified proofs given later by Gowers, and independently, Reingold–Trevisan–Tulsiani–Vadhan) applied with a discrepancy/cut-type norm (instead of a Gowers uniformity norm as it was applied in earlier works); (2) a counting lemma established by Conlon, Fox and the author; and (3) Szemerédi's theorem as a black box.
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KOMLÓS, JÁNOS. "The Blow-up Lemma." Combinatorics, Probability and Computing 8, no. 1-2 (January 1999): 161–76. http://dx.doi.org/10.1017/s0963548398003502.

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Extremal graph theory has a great number of conjectures concerning the embedding of large sparse graphs into dense graphs. Szemerédi's Regularity Lemma is a valuable tool in finding embeddings of small graphs. The Blow-up Lemma, proved recently by Komlós, Sárközy and Szemerédi, can be applied to obtain approximate versions of many of the embedding conjectures. In this paper we review recent developments in the area.
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BERGELSON, VITALY, and INGER J. HÅLAND KNUTSON. "Weak mixing implies weak mixing of higher orders along tempered functions." Ergodic Theory and Dynamical Systems 29, no. 5 (February 26, 2009): 1375–416. http://dx.doi.org/10.1017/s0143385708000862.

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AbstractWe extend the weakly mixing PET (polynomial ergodic theorem) obtained in Bergelson [Weakly mixing PET. Ergod. Th. & Dynam. Sys.7 (1987), 337–349] to much wider families of functions. Besides throwing new light on the question of ‘how much higher-degree mixing is hidden in weak mixing’, the obtained results also show the way to possible new extensions of the polynomial Szemerédi theorem obtained in Bergelson and Leibman [Polynomial extensions of van der Waerden’s and Szemerédi’s theorems. J. Amer. Math. Soc.9 (1996), 725–753].
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Raussen, Martin, and Christian Skau. "Interview with Endre Szemerédi." Notices of the American Mathematical Society 60, no. 02 (February 1, 2013): 1. http://dx.doi.org/10.1090/noti948.

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Conlon, David, Jacob Fox, and Yufei Zhao. "A relative Szemerédi theorem." Geometric and Functional Analysis 25, no. 3 (March 17, 2015): 733–62. http://dx.doi.org/10.1007/s00039-015-0324-9.

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Kehoe, Elaine. "Szemerédi Receives 2012 Abel Prize." Notices of the American Mathematical Society 59, no. 06 (June 1, 2012): 1. http://dx.doi.org/10.1090/noti855.

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Keevash, Peter, and Richard Mycroft. "A multipartite Hajnal–Szemerédi theorem." Journal of Combinatorial Theory, Series B 114 (September 2015): 187–236. http://dx.doi.org/10.1016/j.jctb.2015.04.003.

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Jones, Albin L. "On a result of Szemerédi." Journal of Symbolic Logic 73, no. 3 (September 2008): 953–56. http://dx.doi.org/10.2178/jsl/1230396758.

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AbstractWe provide a short proof that if κ is a regular cardinal with κ < c, thenfor any ordinal α < min{, κ}. In particular,for any ordinal α < . This generalizes an unpublished result of E. Szemerédi that Martin's axiom implies thatfor any cardinal κ with κ < c.
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Adhikari, S. D., L. Boza, S. Eliahou, M. P. Revuelta, and M. I. Sanz. "Numerical semigroups of Szemerédi type." Discrete Applied Mathematics 263 (June 2019): 8–13. http://dx.doi.org/10.1016/j.dam.2018.03.023.

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Han, Jie, and Yi Zhao. "On multipartite Hajnal–Szemerédi theorems." Discrete Mathematics 313, no. 10 (May 2013): 1119–29. http://dx.doi.org/10.1016/j.disc.2013.02.008.

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Dissertations / Theses on the topic "Szemerédi"

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Zhao, Yufei. "Sparse regularity and relative Szemerédi theorems." Thesis, Massachusetts Institute of Technology, 2015. http://hdl.handle.net/1721.1/99060.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 171-179).
We extend various fundamental combinatorial theorems and techniques from the dense setting to the sparse setting. First, we consider Szemerédi regularity lemma, a fundamental tool in extremal combinatorics. The regularity method, in its original form, is effective only for dense graphs. It has been a long standing problem to extend the regularity method to sparse graphs. We solve this problem by proving a so-called "counting lemma," thereby allowing us to apply the regularity method to relatively dense subgraphs of sparse pseudorandom graphs. Next, by extending these ideas to hypergraphs, we obtain a simplification and extension of the key technical ingredient in the proof of the celebrated Green-Tao theorem, which states that there are arbitrarily long arithmetic progressions in the primes. The key step, known as a relative Szemerédi theorem, says that any positive proportion subset of a pseudorandom set of integers contains long arithmetic progressions. We give a simple proof of a strengthening of the relative Szemerédi theorem, showing that a much weaker pseudorandomness condition is sufficient. Finally, we give a short simple proof of a multidimensional Szemerédi theorem in the primes, which states that any positive proportion subset of Pd (where P denotes the primes) contains constellations of any given shape. This has been conjectured by Tao and recently proved by Cook, Magyar, and Titichetrakun and independently by Tao and Ziegler.
by Yufei Zhao.
Ph. D.
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Moretti, Junior Nilton Cesar. "Dinâmica, combinatória e ergodicidade." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/154770.

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Submitted by Nilton Cesar Moretti Junior null (niiilton@hotmail.com) on 2018-07-31T04:58:47Z No. of bitstreams: 1 Dissertação-Final.pdf: 1149444 bytes, checksum: 6c44dc0b9f2462ee08c23da4a240fa0a (MD5)
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Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)
Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)
Neste trabalho estudamos vários resultados relacionados com sistemas dinâmicos, teoria dos números e combinatória. Em particular, provamos os teoremas de Van Der Waerden, Szemeredi, Koksma e Weyl.
In this work we study several results connected with dynamical systems, number thoery and combinatorics. In particular, we prove Van Der Waerden, Szemer edi, Koksma and Weyl’s theorems.
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Beyers, Frederik Johannes Conradie. "The Szemeredi property in noncommutative dynamical systems." Pretoria : [s.n.], 2009. http://upetd.up.ac.za/thesis/available/etd-05242009-145506.

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Titichetrakun, Tatchai. "A multidimensional Szemerédi's theorem in the primes." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/58429.

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In this thesis, we investigate topics related to the Green-Tao theorem on arithmetic progression in primes in higher dimensions. Our main tool is the pseudorandom measure majorizing primes defined in [51] concentrated on almost primes. In chapter 2, we combine the sieve technique used in constructing pseudorandom measure (in this case, Goldston-Yildirim sum and almost primes) with the circle method of Birch to study the number of almost prime solutions of diophantine systems (with some rank conditions). Our rank condition is similar to the integer case, due to the heuristics that almost primes are pseudorandom. In chapter 3, we investigate the generalization of Green-Tao’s theorem to higher dimensions in the case of corner configuration. We apply the transference principle of Green-Tao (with hyperplane separation technique of Gowers) in this setting. This problem is also related to the densification trick in [16]. In chapter 4, we extend the result of Chapter 3 to obtain the full multi-dimensional analogue of the Green-Tao’s theorem, using hypergraph regularity method by directly proving a version of hypergraph removal lemma in the weighted hypergraphs. The method is to run an energy increment on a parametric weight systems of measures, rather than on a single measure space, to overcome the presence of intermediate weights. Contrary to [110], [68] where the authors investigate the problem using a measure supported on primes and infinite linear form conditions, relying on the Gowers Inverse Norms Conjecture.
Science, Faculty of
Mathematics, Department of
Graduate
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Curado, Manuel. "Structural Similarity: Applications to Object Recognition and Clustering." Doctoral thesis, Universidad de Alicante, 2018. http://hdl.handle.net/10045/98110.

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In this thesis, we propose many developments in the context of Structural Similarity. We address both node (local) similarity and graph (global) similarity. Concerning node similarity, we focus on improving the diffusive process leading to compute this similarity (e.g. Commute Times) by means of modifying or rewiring the structure of the graph (Graph Densification), although some advances in Laplacian-based ranking are also included in this document. Graph Densification is a particular case of what we call graph rewiring, i.e. a novel field (similar to image processing) where input graphs are rewired to be better conditioned for the subsequent pattern recognition tasks (e.g. clustering). In the thesis, we contribute with an scalable an effective method driven by Dirichlet processes. We propose both a completely unsupervised and a semi-supervised approach for Dirichlet densification. We also contribute with new random walkers (Return Random Walks) that are useful structural filters as well as asymmetry detectors in directed brain networks used to make early predictions of Alzheimer's disease (AD). Graph similarity is addressed by means of designing structural information channels as a means of measuring the Mutual Information between graphs. To this end, we first embed the graphs by means of Commute Times. Commute times embeddings have good properties for Delaunay triangulations (the typical representation for Graph Matching in computer vision). This means that these embeddings can act as encoders in the channel as well as decoders (since they are invertible). Consequently, structural noise can be modelled by the deformation introduced in one of the manifolds to fit the other one. This methodology leads to a very high discriminative similarity measure, since the Mutual Information is measured on the manifolds (vectorial domain) through copulas and bypass entropy estimators. This is consistent with the methodology of decoupling the measurement of graph similarity in two steps: a) linearizing the Quadratic Assignment Problem (QAP) by means of the embedding trick, and b) measuring similarity in vector spaces. The QAP problem is also investigated in this thesis. More precisely, we analyze the behaviour of $m$-best Graph Matching methods. These methods usually start by a couple of best solutions and then expand locally the search space by excluding previous clamped variables. The next variable to clamp is usually selected randomly, but we show that this reduces the performance when structural noise arises (outliers). Alternatively, we propose several heuristics for spanning the search space and evaluate all of them, showing that they are usually better than random selection. These heuristics are particularly interesting because they exploit the structure of the affinity matrix. Efficiency is improved as well. Concerning the application domains explored in this thesis we focus on object recognition (graph similarity), clustering (rewiring), compression/decompression of graphs (links with Extremal Graph Theory), 3D shape simplification (sparsification) and early prediction of AD.
Ministerio de Economía, Industria y Competitividad (Referencia TIN2012-32839 BES-2013-064482)
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Beyers, Frederik Johannes Conradie. "The Szemerédi property in noncommutative dynamical systems." Thesis, 2009. http://hdl.handle.net/2263/24940.

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No abstract available. Copyright 2008, University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. Please cite as follows: Beyers, FJC 2008, The Szemerédi property in noncommutative dynamical systems, PhD thesis, University of Pretoria, Pretoria, viewed yymmdd < http://upetd.up.ac.za/thesis/available/etd-05242009-145506/ > D620/ag
Thesis (PhD)--University of Pretoria, 2009.
Mathematics and Applied Mathematics
unrestricted
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Hladký, Jan. "Szemerédi Regularity Lemma a jeho aplikace v kombinatorice." Master's thesis, 2008. http://www.nusl.cz/ntk/nusl-294535.

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In the thesis we provide a solution of the Loebl-Komlós-Sós Conjecture (1995) for dense graphs. We prove that for any q > 0 there exists a number n0 N such that for any n > n0 and k > qn the following holds. Let G be a graph of order n with at least n/2 vertices of degree at least k. Then any tree of order k+1 is a subgraph of G. This improves previous results by Zhao (2002), and Piguet and Stein (2007). A strengthened version of the above theorem together with a lower bound for the problem is discussed. As a corollary a tight bound on the Ramsey number of two trees is stated. The proof of the main theorem combines a Regularity-Lemma based embedding technique with the Stability Method of Simonovits. Results presented here are based on joint work with Diana Piguet.
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Pinto, Pedro Miguel dos Santos. "Teorema da estrutura de Furstenberg: demonstração e redução ao nível Www." Master's thesis, 2013. http://hdl.handle.net/10451/10364.

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Tese de mestrado em Matemática, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2013
Esta dissertação tem como tema principal apresentar a prova do Teorema da Estrutura de Furstenberg-Zimmer, que tem como consequência o Teorema de Furstenberg e o seu equivalente de Teoria dos Números, o Teorema de Szemerédi. Começamos por verificar casos particulares, de resolução mais simples, onde o Teorema de Furstenberg é válido: os sistemas weak-mixing e os sistemas compactos. Prossegue-se para uma relativização das propriedades anteriores e mostramos que é sempre possível obter uma sequência transfinita crescente de sistemas satisfazendo o Teorema de Furstenberg, culminando em toda a generalidade no Teorema da Estrutura. Numa segunda parte, iremos mostrar que não necessitamos de toda a força do Teorema da Estrutura para conseguirmos concluir o Teorema de Furstenberg: de facto ao nível ordinal www estamos já em condições suficientes para provar o teorema. Concluímos com algumas considerações sobre a construtividade do Teorema da Estrutura e do Teorema de Szemerédi.
The main subject of this dissertation is to present a proof of the Furstenberg-Zimmer Structure Theorem, from which one can obtain Furstenberg's Theorem and its equivalent number-theoretical version that goes by the name of Szemerédi's Theorem. We start by checking simpler particular cases where the Furstenberg's theorem is true, namely for weak-mixing systems and compact systems. We then proceed to a relativization of the previous properties and show that it is always possible to obtain a transfinite sequence of increasing systems satisfying Furstenberg's theorem, culminating in the most general case, the Structure's Theorem. In a second part, we will show that we do not need the full strength of the Structure Theorem in order to obtain Furstenberg's Theorem: at the ordinal level www we are already able to prove the theorem. We conclude with some considerations about constructivity regarding both the Structure's Theorem and Szemerédi's Theorem.
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Tarigan, Regina Ayunita, and 譚芮妲. "Szemerédi’s Regularity Lemma and Its Applications." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/k693tt.

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碩士
國立中央大學
數學系
105
In this dissertation, the Szemerédi’s Regularity Lemma and its application are studied. This lemma is used to partition a large enough graph into almost equal parts so that the number of edges across the parts is fairly random. On the other hand, Roth's Theorem states that there exists an arithmetic progression with length 3 in a subset in integer with positive upper density. We shall see that it can be proved by using triangle removal lemma, which is an application of Szemerédi’s Regularity Lemma.
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Zirnstein, Heinrich-Gregor. "Formulating Szemerédi's theorem in terms of ultrafilters." 2012. https://ul.qucosa.de/id/qucosa%3A16816.

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Van der Waerden's theorem asserts that if you color the natural numbers with, say, five different colors, then you can always find arbitrarily long sequences of numbers that have the same color and that form an arithmetic progression. Szemerédi's theorem generalizes this statement and asserts that every subset of natural numbers with positive density contains arithmetic progressions of arbitrary length.
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Books on the topic "Szemerédi"

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Társulat, Bolyai János Matematikai, ed. An irregular mind: Szemerédi is 70. Berlin: Springer, 2010.

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Bárány, Imre, and Jozsef Solymosi. An Irregular Mind: Szemerédi is 70. Springer, 2012.

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An Ergodic IP Polynomial Szemeredi Theorem (Memoirs of the American Mathematical Society). American Mathematical Society, 2000.

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Comparative-Historical Linguistics: Indo-European and Finno-Ugric. Papers in honor of Oswald Szemerényi III. John Benjamins Publishing Company, 1993.

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Book chapters on the topic "Szemerédi"

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McCutcheon, Randall. "Two Szemerédi theorems." In Elemental Methods in Ergodic Ramsey Theory, 136–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/bfb0093965.

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Karmani, Rajesh K., Gul Agha, Mark S. Squillante, Joel Seiferas, Marian Brezina, Jonathan Hu, Ray Tuminaro, et al. "Ajtai–Komlós–Szemerédi Sorting Network." In Encyclopedia of Parallel Computing, 16. Boston, MA: Springer US, 2011. http://dx.doi.org/10.1007/978-0-387-09766-4_2379.

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Hajnal, András. "My Early Encounters With Szemerédi." In Bolyai Society Mathematical Studies, 755–58. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-14444-8_23.

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Gowers, W. T. "The Mathematics of Endre Szemerédi." In The Abel Prize 2008-2012, 459–93. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-39449-2_25.

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Holden, Helge, and Ragni Piene. "Curriculum Vitae for Endre Szemerédi." In The Abel Prize 2008-2012, 507–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-39449-2_27.

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Keevash, Peter, and Richard Mycroft. "A multipartite Hajnal-Szemerédi theorem." In The Seventh European Conference on Combinatorics, Graph Theory and Applications, 141–46. Pisa: Scuola Normale Superiore, 2013. http://dx.doi.org/10.1007/978-88-7642-475-5_23.

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Bollobás, Béla, and Vladimir Nikiforov. "An Abstract Szemerédi Regularity Lemma." In Bolyai Society Mathematical Studies, 219–40. Berlin, Heidelberg: Springer Berlin Heidelberg, 2008. http://dx.doi.org/10.1007/978-3-540-85221-6_7.

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Nasso, Mauro Di, Isaac Goldbring, and Martino Lupini. "Triangle Removal and Szemerédi Regularity." In Nonstandard Methods in Ramsey Theory and Combinatorial Number Theory, 173–80. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-17956-4_16.

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Holden, Helge, and Ragni Piene. "List of Publications for Endre Szemerédi." In The Abel Prize 2008-2012, 495–506. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-39449-2_26.

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Austin, Tim. "Ajtai–Szemerédi Theorems over quasirandom groups." In Recent Trends in Combinatorics, 453–84. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-24298-9_19.

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Conference papers on the topic "Szemerédi"

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Bavarian, Mohammad, and Peter W. Shor. "Information Causality, Szemerédi-Trotter and Algebraic Variants of CHSH." In ITCS'15: Innovations in Theoretical Computer Science. New York, NY, USA: ACM, 2015. http://dx.doi.org/10.1145/2688073.2688112.

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Shanmugam, Karthikeyan, Alexandras G. Dimakis, Jaime Llorca, and Antonia M. Tulino. "A unified Ruzsa-Szemerédi framework for finite-length coded caching." In 2017 51st Asilomar Conference on Signals, Systems, and Computers. IEEE, 2017. http://dx.doi.org/10.1109/acssc.2017.8335418.

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Tarigan, Regina Ayunita, and Chun-Yen Shen. "Szemerédi's regularity lemma application on 3-term arithmetic progression." In THE 4TH INDOMS INTERNATIONAL CONFERENCE ON MATHEMATICS AND ITS APPLICATION (IICMA 2019). AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0017419.

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