rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Ramsey Theory for Discrete Structures
  name:
    name part: Prömel, Hans Jürgen.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 232 p. 13 illus. online resource.
  abstract: This monograph covers some of the most important developments in Ramsey theory from its beginnings in the early 20th century via its many breakthroughs to recent important developments in the early 21st century. The book first presents a detailed discussion of the roots of Ramsey theory before offering a thorough discussion of the role of parameter sets. It presents several examples of structures that can be interpreted in terms of parameter sets and features the most fundamental Ramsey-type results for parameter sets: Hales-Jewett's theorem and Graham-Rothschild¹s Ramsey theorem as well as their canonical versions and several applications. Next, the book steps back to the most basic structure, to sets. It reviews classic results as well as recent progress on Ramsey numbers and the asymptotic behavior of classical Ramsey functions. In addition, the chapter presents product versions of Ramsey's theorem, a combinatorial proof of the incompleteness of Peano arithmetic, provides a digression to discrepancy theory, and examines extensions of Ramsey's theorem to larger cardinals. The next chapter features an in-depth treatment of the Ramsey problem for graphs and hypergraphs. It gives an account on the existence of sparse and restricted Ramsey theorem's using sophisticated constructions as well as probabilistic methods. Among others it contains a proof of the induced Graham-Rothschild theorem and the random Ramsey theorem. The book closes with a chapter on one of the recent highlights of Ramsey theory: a combinatorial proof of the density Hales-Jewett theorem. This book provides graduate students as well as advanced researchers with a solid introduction and reference to the field. .
  table of contents: Foreword by Angelika Steger -- Preface -- Conventions -- Part I Roots of Ramsey Theory: 1.1 Ramsey’s theorem -- 1.2 From Hilbert’s cube lemma to Rado’s thesis -- Part II A Starting Point of Ramsey Theory: Parameter Sets: 2.1 Definitions and basic examples -- 2.2 Hales-Jewett’s theorem -- 2.3 Graham-Rothschild’s theorem -- 2.4 Canonical partitions -- Part III Back to the Roots: Sets: 3.1 Ramsey numbers -- 3.2 Rapidly growing Ramsey functions -- 3.3 Product theorems -- 3.4 A quasi Ramsey theorem -- 3.5 Partition relations for cardinal numbers -- Part IV Graphs and Hypergraphs: 4.1 Finite graphs -- 4.2 Infinite graphs -- 4.3 Hypergraphs on parameter sets -- 4.4. Ramsey statements for random graphs -- 4.5 Sparse Ramsey Theorems.- Part V Density Ramsey Theorems: 5.1 Szemerédi’s Theorem -- 5.2 Density Hales-Jewett Theorem -- 5.3 Proof of the density Hales-Jewett theorem -- References -- Index.
  note: by Hans Jürgen Prömel.
  subject:
    topic: Mathematics
  subject:
    topic: Computer science
    topic: Mathematics
  subject:
    topic: Discrete mathematics
  subject:
    topic: Combinatorics
  subject:
    topic: Mathematics
  subject:
    topic: Combinatorics
  subject:
    topic: Discrete Mathematics
  subject:
    topic: Discrete Mathematics in Computer Science
  classification: QA164-167.2
  classification: 511.6
  related item:
    title info:
      title: Springer eBooks
  identifier: 9783319013152
  identifier: http://dx.doi.org/10.1007/978-3-319-01315-2
  record info:
    record creation date: 131204
    record change date: 20151204150717.0
    record identifier: 978-3-319-01315-2