English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We discuss three major classes of theorems in additive and extremal combinatorics: decomposition theorems, approximate structure theorems, and transference principles. We also show how the finite‐dimensional Hahn–Banach theorem can be used to give short and transparent proofs of many results of these kinds. Among the applications of this method is a much shorter proof of one of the major steps in the proof of Green and Tao that the primes contain arbitrarily long arithmetic progressions. In order to explain the role of this step, we include a brief description of the rest of their argument. A similar proof has been discovered independently by Reingold, Trevisan, Tulsiani, and Vadhan (‘Electronic Colloquium on Computational Complexity’,  Dense subsets of pseudorandom sets , Proceedings of 49th IEEE FOCS, 2008).

Decompositions, approximate structure, transference, and the Hahn–Banach theorem