TITLE: RAMSEY THEORY FOR DISCRETE STRUCTURES
PUBLISHER: SPRINGER LANGUAGE: ENGLISH
LINK:
http://is.gd/HOuzav RELEASE TYPE: RETAIL
FORMAT: PDF RELEASE DATE: 2014.03.14
ISBN: 9783319013152 STORE DATE: 2013
SAVED.MONEY: 72 EURO DISKCOUNT: 01 x 05MB
AUTHOR: PROEMEL, HANS JUERGEN
BOOK
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-Rothschild s 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
