Combinatorial number theory and additive group theory
This book collects the material delivered in the 2008 edition of the DocCourse in Combinatorics and Geometry which was devoted to the topic of additive combinatorics. The first two parts, which form the bulk of the volume, contain the two main advanced courses, Additive Group Theory and Non-Unique F...
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| Médium: | Livre numérique |
| Jazyk: | Anglais |
| Vydáno: |
Basel :
Birkhäuser Basel
[20..].
Cham : Springer Nature |
| Vydání: | 1st ed. 2009. |
| Edice: | Advanced Courses in Mathematics / CRM Barcelona
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| On-line přístup: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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Description d'après consultation du 2 février 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Combinatorial number theory and additive group theory, Alfred Geroldinger, Imre Z. Ruzsa, Basel, Birkhäuser, Springer [distributor], 2009, 1 vol. (xi-330 p.), Advanced courses in mathematics - CRM Barcelona, 978-3-7643-8961-1 |
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| 100 | 1 | |a Geroldinger, Alfred. | |
| 245 | 1 | 0 | |a Combinatorial number theory and additive group theory |c Alfred Geroldinger, Imre Z. Ruzsa. |
| 250 | |a 1st ed. 2009. | ||
| 260 | |a Basel : |b Birkhäuser Basel. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Advanced Courses in Mathematics / CRM Barcelona |x 2297-0312 | |
| 500 | |a Description d'après consultation du 2 février 2012 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 505 | 1 | |a Additive Group Theory and Non-unique Factorizations Notation Basic concepts of non-unique factorizations The Davenport constant and first precise arithmetical results The structure of sets of lengths Addition theorems and direct zero-sum problems Inverse zero-sum problems and arithmetical consequences Sumsets and Structure Notation Cardinality inequalities Structure of sets with few sums Location and sumsets Density Measure and topology Exercises Thematic seminars A survey on additive and multiplicative decompositions of sumsets and of shifted sets On the detailed structure of sets with small additive property The isoperimetric method Additive structure of difference sets The polynomial method in additive combinatorics Problems in additive number theory, III Incidences and the spectra of graphs Multi-dimensional inverse additive problems. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a This book collects the material delivered in the 2008 edition of the DocCourse in Combinatorics and Geometry which was devoted to the topic of additive combinatorics. The first two parts, which form the bulk of the volume, contain the two main advanced courses, Additive Group Theory and Non-Unique Factorizations by Alfred Geroldinger, and Sumsets and Structure by Imre Z. Ruzsa. The first part centers on the interaction between non-unique factorization theory and additive group theory. The main objective of factorization theory is a systematic treatment of phenomena related to the non-uniqueness of factorizations in monoids and domains. This part introduces basic concepts of factorization theory such as sets of lengths, and outlines the translation of arithmetical questions in Krull monoids into combinatorial questions on zero-sum sequences over the class group. Using methods from additive group theory such as the theorems of Kneser and of Kemperman-Scherk, classical zero-sum constants are studied, including the Davenport constant and the Erdös-Ginzburg-Ziv constant. Finally these results are applied again to the starting arithmetical problems. The second part is a course on the basics of combinatorial number theory (or additive combinatorics): cardinality inequalities (Plünnecke's graph theoretical method), Freiman's theorem on the structure of sets with a small sumset, inequalities for the Schnirelmann and asymptotic density of sumsets, analogous results for the measure of sumsets of reals, the connection with the Bohr topology. The third part of the volume collects some of the seminars which accompanied the main courses. It contains contributions by C. Elsholtz, G. Freiman, Y. O. Hamidoune, N. Hegyvari, G. Karolyi, M. Nathanson, J. Solymosi and Y. Stanchescu. | ||
| 650 | |a Combinatoire additive | ||
| 650 | |a Théorie combinatoire des nombres | ||
| 650 | |a Groupes, Théorie des | ||
| 700 | 1 | |a Ruzsa, Imre Z., |d 1953- |4 aut | |
| 776 | 0 | |0 134092317 |t Combinatorial number theory and additive group theory |f Alfred Geroldinger, Imre Z. Ruzsa |c Basel |n Birkhäuser |n Springer [distributor] |d 2009 |p 1 vol. (xi-330 p.) |s Advanced courses in mathematics - CRM Barcelona |z 978-3-7643-8961-1 | |
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