Additive number theory inverse problems and the geometry of sumsets
Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer h[actual symbol not reproducible]2 and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. In contrast, in an inverse prob...
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| Format: | Buch |
| Sprache: | English |
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New York [u.a.]
Springer
1996
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| Schriftenreihe: | Graduate texts in mathematics
165 |
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| 245 | 1 | 0 | |a Additive number theory |b inverse problems and the geometry of sumsets |c Melvyn B. Nathanson |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1996 | |
| 300 | |a XIV, 293 S. |b graph. Darst. | ||
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| 490 | 1 | |a Graduate texts in mathematics |v 165 | |
| 520 | 3 | |a Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer h[actual symbol not reproducible]2 and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. In contrast, in an inverse problem, one starts with a sumset hA and attempts to describe the structure of the underlying set A. In recent years, there has been remarkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plunnecke, Vospel and others. This volume includes their results and culminates with an elegant proof by Rusza of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression | |
| 520 | |a Inverse problems are a central topic in additive number theory. This graduate text gives a comprehensive and self-contained account of this subject. In particular, it contains complete proofs of results from exterior algebra, combinatorics, graph theory, and the geometry of numbers that are used in the proofs of the principal inverse theorems. The only prerequisites for the book are undergraduate courses in algebra, number theory, and analysis | ||
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Datensatz im Suchindex
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| ctrlnum | (OCoLC)34471461 (DE-599)BVBBV010997259 |
| dewey-full | 512/.73 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512 273 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV010997259 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:02:20Z |
| institution | BVB |
| isbn | 0387946551 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007361693 |
| oclc_num | 34471461 |
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| physical | XIV, 293 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Springer |
| record_format | marc |
| series | Graduate texts in mathematics |
| series2 | Graduate texts in mathematics |
| spelling | Nathanson, Melvyn B. Verfasser aut Additive number theory inverse problems and the geometry of sumsets Melvyn B. Nathanson New York [u.a.] Springer 1996 XIV, 293 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate texts in mathematics 165 Many classical problems in additive number theory are direct problems, in which one starts with a set A of natural numbers and an integer h[actual symbol not reproducible]2 and tries to describe the structure of the sumset hA consisting of all sums of h elements of A. In contrast, in an inverse problem, one starts with a sumset hA and attempts to describe the structure of the underlying set A. In recent years, there has been remarkable progress in the study of inverse problems for finite sets of integers. In particular, there are important and beautiful inverse theorems due to Freiman, Kneser, Plunnecke, Vospel and others. This volume includes their results and culminates with an elegant proof by Rusza of the deep theorem of Freiman that a finite set of integers with a small sumset must be a large subset of an n-dimensional arithmetic progression Inverse problems are a central topic in additive number theory. This graduate text gives a comprehensive and self-contained account of this subject. In particular, it contains complete proofs of results from exterior algebra, combinatorics, graph theory, and the geometry of numbers that are used in the proofs of the principal inverse theorems. The only prerequisites for the book are undergraduate courses in algebra, number theory, and analysis Getaltheorie gtt Nombres, Théorie des Nombres, Théorie des ram Number theory Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Additive Zahlentheorie (DE-588)4141387-8 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s DE-604 Additive Zahlentheorie (DE-588)4141387-8 s Graduate texts in mathematics 165 (DE-604)BV000000067 165 |
| spellingShingle | Nathanson, Melvyn B. Additive number theory inverse problems and the geometry of sumsets Graduate texts in mathematics Getaltheorie gtt Nombres, Théorie des Nombres, Théorie des ram Number theory Zahlentheorie (DE-588)4067277-3 gnd Additive Zahlentheorie (DE-588)4141387-8 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4141387-8 |
| title | Additive number theory inverse problems and the geometry of sumsets |
| title_auth | Additive number theory inverse problems and the geometry of sumsets |
| title_exact_search | Additive number theory inverse problems and the geometry of sumsets |
| title_full | Additive number theory inverse problems and the geometry of sumsets Melvyn B. Nathanson |
| title_fullStr | Additive number theory inverse problems and the geometry of sumsets Melvyn B. Nathanson |
| title_full_unstemmed | Additive number theory inverse problems and the geometry of sumsets Melvyn B. Nathanson |
| title_short | Additive number theory |
| title_sort | additive number theory inverse problems and the geometry of sumsets |
| title_sub | inverse problems and the geometry of sumsets |
| topic | Getaltheorie gtt Nombres, Théorie des Nombres, Théorie des ram Number theory Zahlentheorie (DE-588)4067277-3 gnd Additive Zahlentheorie (DE-588)4141387-8 gnd |
| topic_facet | Getaltheorie Nombres, Théorie des Number theory Zahlentheorie Additive Zahlentheorie |
| volume_link | (DE-604)BV000000067 |
| work_keys_str_mv | AT nathansonmelvynb additivenumbertheoryinverseproblemsandthegeometryofsumsets |