Ramsey Theory for Discrete Structures

Nonfiction, Science & Nature, Mathematics, Combinatorics, Discrete Mathematics
Cover of the book Ramsey Theory for Discrete Structures by Hans Jürgen Prömel, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Hans Jürgen Prömel ISBN: 9783319013152
Publisher: Springer International Publishing Publication: December 4, 2013
Imprint: Springer Language: English
Author: Hans Jürgen Prömel
ISBN: 9783319013152
Publisher: Springer International Publishing
Publication: December 4, 2013
Imprint: Springer
Language: English

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, it 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 part of the book 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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, it 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 part of the book 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.

More books from Springer International Publishing

Cover of the book Applied Logic for Computer Scientists by Hans Jürgen Prömel
Cover of the book The Political Theology of European Integration by Hans Jürgen Prömel
Cover of the book Image and Graphics by Hans Jürgen Prömel
Cover of the book Accountability, Transparency and Democracy in the Functioning of Bretton Woods Institutions by Hans Jürgen Prömel
Cover of the book Power Systems Resilience by Hans Jürgen Prömel
Cover of the book Nonlinearity: Ordinary and Fractional Approximations by Sublinear and Max-Product Operators by Hans Jürgen Prömel
Cover of the book Informatics in Schools. Fundamentals of Computer Science and Software Engineering by Hans Jürgen Prömel
Cover of the book Sex Workers and Criminalization in North America and China by Hans Jürgen Prömel
Cover of the book New Civil Codes in Hungary and Romania by Hans Jürgen Prömel
Cover of the book Sedimentation in the Rupnarayan River by Hans Jürgen Prömel
Cover of the book Clinical Anesthesia by Hans Jürgen Prömel
Cover of the book Building Energy Performance Assessment in Southern Europe by Hans Jürgen Prömel
Cover of the book Principles of Orthopedic Practice for Primary Care Providers by Hans Jürgen Prömel
Cover of the book My Search for Ramanujan by Hans Jürgen Prömel
Cover of the book Functional Molecular Silicon Compounds I by Hans Jürgen Prömel
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy