Preface to the Second
As noted in the preface of the first edition, one of the book’s pri-
mary purposes is to serve as a source of unsolved problems in the
flourishing and relatively “wide-open” area of Ramsey theory on the
integers. We especially hoped the book would provide beginning re-
searchers, including graduate students and undergraduate students,
with a range of accessible topics in which to delve. It seems that
we have already been at least somewhat successful because, since the
publication of the first edition, a good number of the research prob-
lems have been solved or partially solved, and several of the theorems
have been improved upon. As a consequence, the new edition includes
many substantial revisions and additions.
Various new sections have been added and others have been sig-
nificantly updated. Among the newly introduced topics are: rainbow
Ramsey theory, an “inequality” version of Schur’s theorem, monochro-
matic solutions of recurrence relations, Ramsey results involving both
sums and products, monochromatic sets avoiding certain differences,
Ramsey properties for polynomial progressions, generalizations of the
Erd˝ os-Ginzberg-Ziv theorem, and the number of arithmetic progres-
sions under arbitrary colorings. We also offer many new results and
proofs among the topics that are not new to this edition, most of
Previous Page Next Page