# Ramsey Theory on the Integers: Second Edition

American Mathematical Soc., 10 nov. 2014 - 384 pages

Ramsey theory is the study of the structure of mathematical objects that is preserved under partitions. In its full generality, Ramsey theory is quite powerful, but can quickly become complicated. By limiting the focus of this book to Ramsey theory applied to the set of integers, the authors have produced a gentle, but meaningful, introduction to an important and enticing branch of modern mathematics. Ramsey Theory on the Integers offers students a glimpse into the world of mathematical research and the opportunity for them to begin pondering unsolved problems.

For this new edition, several sections have been added and others have been significantly updated. Among the newly introduced topics are: rainbow Ramsey theory, an "inequality" version of Schur's theorem, monochromatic solutions of recurrence relations, Ramsey results involving both sums and products, monochromatic sets avoiding certain differences, Ramsey properties for polynomial progressions, generalizations of the Erdős-Ginzberg-Ziv theorem, and the number of arithmetic progressions under arbitrary colorings. Many new results and proofs have been added, most of which were not known when the first edition was published. Furthermore, the book's tables, exercises, lists of open research problems, and bibliography have all been significantly updated.

This innovative book also provides the first cohesive study of Ramsey theory on the integers. It contains perhaps the most substantial account of solved and unsolved problems in this blossoming subject. This breakthrough book will engage students, teachers, and researchers alike.

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### Table des matières

 Other Topics 10 Van der Waerdens Theorem 23 2 7 36 On the Number of Monochromatic Arithmetic 51 Exercises 57 Supersets of 67 Notation 69 Subsets of 113
 Exercises 177 Arithmetic Progressions modm 183 Other Variations on van der Waerdens Theorem 203 Schurs Theorem 221 Rados Theorem 251 3 9 367 239 371 328 376

 Other Generalizations of wkr 147
 Droits d'auteur

### À propos de l'auteur (2014)

Bruce M. Landman, State University of West Georgia, Carrollton, GA, USA.

Aaron Robertson, Colgate University, Hamilton, NY, USA.