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020 _a9783642729058
_9978-3-642-72905-8
024 7 _a10.1007/978-3-642-72905-8
_2doi
050 4 _aQA164-167.2
072 7 _aPBV
_2bicssc
072 7 _aMAT036000
_2bisacsh
072 7 _aPBV
_2thema
082 0 4 _a511.6
245 1 0 _aMathematics of Ramsey Theory
_h[electronic resource] /
_cedited by Jaroslav Nesetril, Vojtech Rödl.
250 _a1st ed. 1990.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg :
_bImprint: Springer,
_c1990.
300 _aXIV, 269 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aAlgorithms and Combinatorics,
_x0937-5511 ;
_v5
505 0 _aRamsey Theory Old and New -- 1. Ramsey Numbers -- 2. Transfinite Ramsey Theory -- 3. Chromatic Number -- 4. Classical Theorems -- 5. Other Classical Theorems -- 6. Structural Generalizations -- 7. Infinite Ramsey Theorem -- 8. Unprovability Results -- 9. Non-Standard Applications -- I. Classics -- Problems and Results on Graphs and Hypergraphs: Similarities and Differences -- Note on Canonical Partitions -- II. Numbers -- On Size Ramsey Number of Paths, Trees and Circuits. II -- On the Computational Complexity of Ramsey-Type Problems -- Constructive Ramsey Bounds and Intersection Theorems for Sets -- Ordinal Types in Ramsey Theory and Well-Partial-Ordering Theory -- III. Structural Theory -- Partite Construction and Ramsey Space Systems -- Graham-Rothschild Parameter Sets -- Shelah's Proof of the Hales-Jewett Theorem -- IV. Noncombinatorial Methods -- Partitioning Topological Spaces -- Topological Ramsey Theory -- Ergodic Theory and Configurations in Sets of Positive Density -- V. Variations and Applications -- Topics in Euclidean Ramsey Theory -- On Pisier Type Problems and Results (Combinatorial Applications to Number Theory) -- Combinatorial Statements Independent of Arithmetic -- Boolean Complexity and Ramsey Theorems -- Uncrowded Graphs -- Author Index.
520 _aOne of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and survey articles by leading specialists. It surveys recent activity in this diverse subject and brings the reader up to the boundary of present knowledge. It covers virtually all main approaches to the subject and suggests various problems for individual research.
650 0 _aCombinatorics.
650 0 _aMathematical logic.
650 0 _aEconomic theory.
650 1 4 _aCombinatorics.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M29010
650 2 4 _aMathematical Logic and Foundations.
_0https://scigraph.springernature.com/ontologies/product-market-codes/M24005
650 2 4 _aEconomic Theory/Quantitative Economics/Mathematical Methods.
_0https://scigraph.springernature.com/ontologies/product-market-codes/W29000
700 1 _aNesetril, Jaroslav.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aRödl, Vojtech.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783642729072
776 0 8 _iPrinted edition:
_z9783540181910
776 0 8 _iPrinted edition:
_z9783642729065
776 0 8 _iPrinted edition:
_z9783662602348
830 0 _aAlgorithms and Combinatorics,
_x0937-5511 ;
_v5
856 4 0 _uhttps://s443-doi-org.br.lsproxy.net/10.1007/978-3-642-72905-8
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