By David Grynkiewicz

ISBN-10: 3319004158

ISBN-13: 9783319004150

ISBN-10: 3319375180

ISBN-13: 9783319375182

Nestled among quantity thought, combinatorics, algebra and research lies a quickly constructing topic in arithmetic variously referred to as additive combinatorics, additive quantity thought, additive workforce concept, and combinatorial quantity thought. Its major items of analysis usually are not abelian teams themselves, yet relatively the additive constitution of subsets and subsequences of an abelian workforce, i.e., sumsets and subsequence sums. this article is a hybrid of a study monograph and an introductory graduate textbook. With few exceptions, all effects provided are self-contained, written in nice aspect, and merely reliant upon fabric coated in a sophisticated undergraduate curriculum supplemented with a few extra Algebra, rendering this book usable as an entry-level textual content. although, it is going to possibly be of much more curiosity to researchers already within the box. the vast majority of fabric isn't really present in e-book shape and contains many new effects to boot. Even classical effects, whilst incorporated, are given in higher generality or utilizing new evidence adaptations. The textual content has a specific specialise in result of a extra detailed and exact nature, effects with powerful hypotheses and but enhanced conclusions, and on primary facets of the speculation. additionally integrated are problematic effects usually overlooked in different texts because of their complexity. Highlights contain an intensive therapy of Freiman Homomorphisms and the common Ambient team of sumsets A+B, a whole bankruptcy dedicated to Hamidoune’s Isoperimetric strategy, a unique generalization permitting endless summands in finite sumset questions, weighted zero-sum difficulties taken care of within the common context of viewing homomorphisms as weights, and simplified proofs of the Kemperman constitution Theorem and the Partition Theorem for setpartitions.