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Additive Combinatorics
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  • Cited by 209
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    This (lowercase (translateProductType product.productType)) has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Götze, Friedrich and Zaitsev, Andrei Yu. 2018. New applications of Arak’s inequalities to the Littlewood–Offord problem. European Journal of Mathematics,


    Madiman, Mokshay and Kontoyiannis, Ioannis 2018. Entropy Bounds on Abelian Groups and the Ruzsa Divergence. IEEE Transactions on Information Theory, Vol. 64, Issue. 1, p. 77.


    Cwalina, Karol and Schoen, Tomasz 2017. Tight bounds on additive Ramsey-type numbers. Journal of the London Mathematical Society, Vol. 96, Issue. 3, p. 601.


    Dyatlov, Semyon and Jin, Long 2017. Resonances for Open Quantum Maps and a Fractal Uncertainty Principle. Communications in Mathematical Physics, Vol. 354, Issue. 1, p. 269.


    Chi, Zhiyi 2017. On a Multivariate Strong Renewal Theorem. Journal of Theoretical Probability,


    Garaev, M. Z. and Hernández, J. 2017. A note on n! modulo p. Monatshefte für Mathematik, Vol. 182, Issue. 1, p. 23.


    Green, Ben and Tao, Terence 2017. NEW BOUNDS FOR SZEMERÉDI’S THEOREM, III: A POLYLOGARITHMIC BOUND FOR . Mathematika, Vol. 63, Issue. 03, p. 944.


    Shteinikov, Yurii N. 2017. On the product sets of rational numbers. Proceedings of the Steklov Institute of Mathematics, Vol. 296, Issue. 1, p. 243.


    Madiman, Mokshay Melbourne, James and Xu, Peng 2017. Convexity and Concentration. Vol. 161, Issue. , p. 427.

    Semchankau, A. S. 2017. Maximal subsets free of arithmetic progressions in arbitrary sets. Mathematical Notes, Vol. 102, Issue. 3-4, p. 396.


    Shkredov, I. D. 2017. Some remarks on the Balog–Wooley decomposition theorem and quantities D +, D × . Proceedings of the Steklov Institute of Mathematics, Vol. 298, Issue. S1, p. 74.


    Tao, Terence and Vu, Van 2017. Random matrices have simple spectrum. Combinatorica, Vol. 37, Issue. 3, p. 539.


    Volostnov, A. S. and Shkredov, I. D. 2017. Sums of multiplicative characters with additive convolutions. Proceedings of the Steklov Institute of Mathematics, Vol. 296, Issue. 1, p. 256.


    Stevens, Sophie and de Zeeuw, Frank 2017. An improved point-line incidence bound over arbitrary fields. Bulletin of the London Mathematical Society, Vol. 49, Issue. 5, p. 842.


    Geelen, Jim and Nelson, Peter 2017. Odd circuits in dense binary matroids. Combinatorica, Vol. 37, Issue. 1, p. 41.


    BACHOC, CHRISTINE SERRA, ORIOL and ZÉMOR, GILLES 2017. An analogue of Vosper's theorem for extension fields. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 163, Issue. 03, p. 423.


    Шкредов, Илья Дмитриевич and Shkredov, Ilya Dmitrievich 2017. Несколько замечаний к теореме о разложимости Балога - Вули и величинах $D^{+}$, $D^\times$. Современные проблемы математики, Vol. 24, p. 85.


    Herdade, Simao Kim, John and Koppartyy, Swastik 2017. A Cauchy-Davenport theorem for linear maps. Combinatorica,


    Вьюгин, Илья Владимирович Vyugin, Il'ya Vladimirovich Солодкова, Е В Solodkova, E V Шкредов, Илья Дмитриевич and Shkredov, Ilya Dmitrievich 2017. Об аддитивной энергии подгруппы Хейльбронна. Математические заметки, Vol. 101, Issue. 1, p. 43.


    Bachoc, Christine Serra, Oriol and Zémor, Gilles 2017. Revisiting Kneser’s theorem for field extensions. Combinatorica,


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    Additive Combinatorics
    • Online ISBN: 9780511755149
    • Book DOI: https://doi.org/10.1017/CBO9780511755149
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Book description

Additive combinatorics is the theory of counting additive structures in sets. This theory has seen exciting developments and dramatic changes in direction in recent years thanks to its connections with areas such as number theory, ergodic theory and graph theory. This graduate-level 2006 text will allow students and researchers easy entry into this fascinating field. Here, the authors bring together in a self-contained and systematic manner the many different tools and ideas that are used in the modern theory, presenting them in an accessible, coherent, and intuitively clear manner, and providing immediate applications to problems in additive combinatorics. The power of these tools is well demonstrated in the presentation of recent advances such as Szemerédi's theorem on arithmetic progressions, the Kakeya conjecture and Erdos distance problems, and the developing field of sum-product estimates. The text is supplemented by a large number of exercises and new results.

Reviews

'The book under review is a vital contribution to the literature, and it has already become required reading for a new generation of students as well as for experts in adjacent areas looking to learn about additive combinatorics. … This was very much a book that needed to be written at the time it was, and the authors are to be highly commended for having done so in such an effective way.'

Source: Bulletin of the American Mathematical Society

'The book gathers diverse important techniques used in additive combinatorics, and its main advantage is that it is written in a very readable and easy to understand style. The authors try very successfully to develop all the necessary background material … [which] makes the book useful not only to graduate students, but also to researchers who are interested to learn more about the variety of diverse tools and ideas applied in this fascinating subject.'

Source: Zentralblatt MATH

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