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008			150903s2009 sz | o |||| 0|eng d
020			_a9783764389628 _99783764389628
024	7		_a10.1007/9783764389628 _2doi
035			_avtls000363004
039		9	_a201509031021 _bVLOAD _c201405070338 _dVLOAD _y201402211137 _zstaff
040			_aMX-SnUAN _bspa _cMX-SnUAN _erda
050		4	_aQA164-167.2
100	1		_aGeroldinger, Alfred. _eautor _9350458
245	1	0	_aCombinatorial Number Theory and Additive Group Theory / _cby Alfred Geroldinger, Imre Z. Ruzsa.
264		1	_aBasel : _bBirkhäuser Basel, _c2009.
300			_brecurso en línea.
336			_atexto _btxt _2rdacontent
337			_acomputadora _bc _2rdamedia
338			_arecurso en línea _bcr _2rdacarrier
347			_aarchivo de texto _bPDF _2rda
490	0		_aAdvanced Courses in Mathematics - CRM Barcelona, Centre de Recerca Matemàtica
500			_aSpringer eBooks
505	0		_aAdditive 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.
520			_aThis 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.
590			_aPara consulta fuera de la UANL se requiere clave de acceso remoto.
700	1		_aRuzsa, Imre Z. _eautor _9350459
710	2		_aSpringerLink (Servicio en línea) _9299170
776	0	8	_iEdición impresa: _z9783764389611
856	4	0	_uhttp://remoto.dgb.uanl.mx/login?url=http://dx.doi.org/10.1007/978-3-7643-8962-8 _zConectar a Springer E-Books (Para consulta externa se requiere previa autentificación en Biblioteca Digital UANL)
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999			_c309944 _d309944