LEADER 04807nam 22007095 450 001 9910741183603321 005 20251113211745.0 010 $a9783319004167 010 $a3319004166 024 7 $a10.1007/978-3-319-00416-7 035 $a(CKB)2670000000371286 035 $a(EBL)1317201 035 $a(SSID)ssj0000904272 035 $a(PQKBManifestationID)11595432 035 $a(PQKBTitleCode)TC0000904272 035 $a(PQKBWorkID)10938982 035 $a(PQKB)11166833 035 $a(DE-He213)978-3-319-00416-7 035 $a(MiAaPQ)EBC1317201 035 $a(PPN)170489744 035 $a(MiFhGG)9783319004167 035 $a(EXLCZ)992670000000371286 100 $a20130531d2013 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStructural Additive Theory /$fby David J. Grynkiewicz 205 $a1st ed. 2013. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2013. 215 $a1 online resource (425 p.) 225 1 $aDevelopments in Mathematics,$x2197-795X ;$v30 300 $aDescription based upon print version of record. 311 08$a9783319004150 311 08$a3319004158 320 $aIncludes bibliographical references and index. 327 $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 ?-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. 330 $aNestled between number theory, combinatorics, algebra, and analysis lies a rapidly developing subject in mathematics variously known as additive combinatorics, additive number theory, additive group theory, and combinatorial number theory. Its main objects of study are not abelian groups themselves, but rather the additive structure of subsets and subsequences of an abelian group, i.e. sumsets and subsequence sums. This text is a hybrid of a research monograph and an introductory graduate textbook. With few exceptions, all results presented are self-contained, written in great detail, and only reliant upon material covered in an advanced undergraduate curriculum supplemented with some additional Algebra, rendering this book usable as an entry-level text. However, it will perhaps be of even more interest to researchers already in the field. The majority of material is not found in book form and includes many new results as well. Even classical results, when included, are given in greater generality or using new proof variations. The text has a particular focus on results of a more exact and precise nature, results with strong hypotheses and yet stronger conclusions, and on fundamental aspects of the theory. Also included are intricate results often neglected in other texts owing to their complexity. Highlights include an extensive treatment of Freiman Homomorphisms and the Universal Ambient Group of sumsets A+B, an entire chapter devoted to Hamidoune?s Isoperimetric Method, a novel generalization allowing infinite summands in finite sumset questions, weighted zero-sum problems treated in the general context of viewing homomorphisms as weights, and simplified proofs of the Kemperman Structure Theorem and the Partition Theorem for setpartitions.  . 410 0$aDevelopments in Mathematics,$x2197-795X ;$v30 606 $aNumber theory 606 $aSequences (Mathematics) 606 $aAlgebra 606 $aNumber Theory 606 $aSequences, Series, Summability 606 $aOrder, Lattices, Ordered Algebraic Structures 615 0$aNumber theory. 615 0$aSequences (Mathematics). 615 0$aAlgebra. 615 14$aNumber Theory. 615 24$aSequences, Series, Summability. 615 24$aOrder, Lattices, Ordered Algebraic Structures. 676 $a512 676 $a512.814 700 $aGrynkiewicz$b David J$01064686 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910741183603321 996 $aStructural additive theory$93554196 997 $aUNINA