Ramsey Theory on the Integers

Bruce M. Landman, Aaron Robertson (Autoren)

Buch | Softcover

384 Seiten

2014 | Second Edition
American Mathematical Society (Verlag)
978-0-8218-9867-3 (ISBN)

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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 Erdos-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.

Bruce M. Landman, State University of West Georgia, Carrollton, GA, USA. Aaron Robertson, Colgate University, Hamilton, NY, USA.

Preliminaries
Van der Waerden's theorem
Supersets of AP
Subsets of AP
Other generalizations of w(k;r)
Arithmetic progressions (mod m)
Other variations on van der Waerden's theorem
Schur's theorem
Rado's theorem
Other topics
Notation
Bibliography
Index

Erscheint lt. Verlag	30.12.2014
Reihe/Serie	Student Mathematical Library
Verlagsort	Providence
Sprache	englisch
Maße	140 x 216 mm
Gewicht	486 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
ISBN-10	0-8218-9867-1 / 0821898671
ISBN-13	978-0-8218-9867-3 / 9780821898673
Zustand	Neuware