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 Bhagavad Gītā and Leadership by Hans Jürgen Prömel
Cover of the book Quick Guide to Good Clinical Practice by Hans Jürgen Prömel
Cover of the book Globalisation and Higher Education Reforms by Hans Jürgen Prömel
Cover of the book Business and Society by Hans Jürgen Prömel
Cover of the book Redox-Active Therapeutics by Hans Jürgen Prömel
Cover of the book Planar Waveguide Optical Sensors by Hans Jürgen Prömel
Cover of the book Model-Driven Engineering and Software Development by Hans Jürgen Prömel
Cover of the book Oncological PET/CT with Histological Confirmation by Hans Jürgen Prömel
Cover of the book Design, User Experience, and Usability: Users, Contexts and Case Studies by Hans Jürgen Prömel
Cover of the book Handbook of Relapsing-Remitting Multiple Sclerosis by Hans Jürgen Prömel
Cover of the book Well-being, Poverty and Justice from a Child’s Perspective by Hans Jürgen Prömel
Cover of the book Turnpike Theory of Continuous-Time Linear Optimal Control Problems by Hans Jürgen Prömel
Cover of the book Computer Algebra in Scientific Computing by Hans Jürgen Prömel
Cover of the book Clinical Psychology and the Philosophy of Science by Hans Jürgen Prömel
Cover of the book PET/CT in Prostate Cancer 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