000 04278nam a22004815i 4500
001 978-3-319-00416-7
003 DE-He213
005 20140220082838.0
007 cr nn 008mamaa
008 130531s2013 gw | s |||| 0|eng d
020 _a9783319004167
_9978-3-319-00416-7
024 7 _a10.1007/978-3-319-00416-7
_2doi
050 4 _aQA241-247.5
072 7 _aPBH
_2bicssc
072 7 _aMAT022000
_2bisacsh
082 0 4 _a512.7
_223
100 1 _aGrynkiewicz, David J.
_eauthor.
245 1 0 _aStructural Additive Theory
_h[electronic resource] /
_cby David J. Grynkiewicz.
264 1 _aHeidelberg :
_bSpringer International Publishing :
_bImprint: Springer,
_c2013.
300 _aXII, 426 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aDevelopments in Mathematics,
_x1389-2177 ;
_v30
505 0 _a1. Abelian Groups and Character Sums -- 2. Introduction to Sumsets -- 3. Simple Results for Torsion-Free Abelian Groups -- 4. Basic Results for Sumsets with an Infinite Summand -- 5. The Pigeonhole and Multiplicity Bounds -- 6. Periodic Sets and Kneser's Theorem -- 7. Compression, Complements and the 3k–4 Theorem -- 8. Additive Energy -- 9. Kemperman's Critical Pair Theory -- 10. Zero-Sums, Setpartitions and Subsequence Sums -- 11. Long Zero-Sum Free Sequences over Cyclic Groups -- 12. Pollard's Theorem for General Abelian Groups -- 13. The DeVos–Goddyn–Mohar Theorem -- 14. The Partition Theorem I -- 15. The Partition Theorem II -- 16. The Ψ-Weighted Gao Theorem -- 17. Group Algebras -- 18. Character and Linear Algebraic Methods -- 19. Character Sum and Fourier Analytic Methods -- 20. Freiman Homomorphisms Revisited -- 21. The Isoperimetric Method -- 22. The Polynomial Method -- Index.
520 _aNestled between number theory, combinatorics, algebra, and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e. sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune’s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.  
650 0 _aMathematics.
650 0 _aAlgebra.
650 0 _aSequences (Mathematics).
650 0 _aNumber theory.
650 1 4 _aMathematics.
650 2 4 _aNumber Theory.
650 2 4 _aSequences, Series, Summability.
650 2 4 _aOrder, Lattices, Ordered Algebraic Structures.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319004150
830 0 _aDevelopments in Mathematics,
_x1389-2177 ;
_v30
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-00416-7
912 _aZDB-2-SMA
999 _c96423
_d96423