Ramsey Theory on the Integers: Second Edition

Couverture
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

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À propos de l'auteur (2014)

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

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

Informations bibliographiques