Ramsey理論是對(duì)數(shù)學(xué)對(duì)象的結(jié)構(gòu)的研究，這本創(chuàng)新的書(shū)提供了Ramsey理論對(duì)整數(shù)的第一個(gè)有凝聚力的研究。它可能包含了這個(gè)蓬勃發(fā)展的學(xué)科中已解決和未解決問(wèn)題的最實(shí)質(zhì)性的說(shuō)明。本書(shū)適合對(duì)組合學(xué)、數(shù)論和Ramsey理論感興趣的研究生和數(shù)學(xué)研究人員閱讀參考。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 Erd？s-Ginzberg-Ziv theorem， and the number of arithmetic progressions under arbitrary colorings.
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