Additive Structures And Randomness In Combinatorics
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Additive Combinatorics
Author: Terence Tao
language: en
Publisher: Cambridge University Press
Release Date: 2006-09-14
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.
Graph Theory and Additive Combinatorics
Author: Yufei Zhao
language: en
Publisher: Cambridge University Press
Release Date: 2023-08-31
An introductory text covering classical and modern developments in graph theory and additive combinatorics, based on Zhao's MIT course.
Geometry, Structure and Randomness in Combinatorics
This book collects some surveys on current trends in discrete mathematics and discrete geometry. The areas covered include: graph representations, structural graphs theory, extremal graph theory, Ramsey theory and constrained satisfaction problems.