Combinatorics

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By Terence Tao,Van H. Vu

Additive combinatorics is the speculation of counting additive constructions in units. This conception has obvious interesting advancements and dramatic adjustments in path in recent times due to its connections with components equivalent to quantity concept, ergodic conception and graph conception. This graduate-level 2006 textual content will let scholars and researchers effortless access into this interesting box. the following, the authors assemble in a self-contained and systematic demeanour the various varied instruments and ideas which are utilized in the fashionable idea, proposing them in an available, coherent, and intuitively transparent demeanour, and supplying rapid functions to difficulties in additive combinatorics. the ability of those instruments is definitely confirmed within the presentation of modern advances reminiscent of Szemerédi's theorem on mathematics progressions, the Kakeya conjecture and Erdos distance difficulties, and the constructing box of sum-product estimates. The textual content is supplemented via loads of routines and new results.

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