By Khodakhast Bibak | published 2011-08-29 |
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Recently, additive combinatorics has blossomed into a vibrant area in
mathematical sciences. But it seems to be a difficult area to define; maybe
because of a blend of ideas and techniques from several seemingly unrelated
contexts which are used there. One might say that additive combinatorics is a
branch of mathematics concerning the study of additive structures in sets
equipped with a group structure; and perhaps other structure that interacts
with the group structure. This newly emerging field has seen tremendous
advancements over the last few years, and has recently become a focus of
attention amongst both mathematicians and computer scientists. This fascinating
area has been enriched by its formidable links to combinatorics, number theory,
harmonic analysis, ergodic theory, and some other branches; all deeply
cross-fertilize each other holding great promise for all of them! There is a
considerable number of incredible problems, results, and novel applications in
this thriving area. In this exposition, we attempt to provide an illuminating
overview of some conspicuous breakthroughs in this captivating field, together
with a number of seminal applications to sundry parts of mathematics and some
other disciplines, with emphasis on computer science and cryptography.
... http://arxiv.org/abs/1108.3790
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