Some Ramsey-type results for the n

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• 作者：Ron Graham ; Jozsef Solymosi
• 关键词：Ramsey Theory ; Monochromatic corners ; Hales– ; Jewett Theorem
• 刊名：Journal of Combinatorial Theory, Series A
• 出版年：2010
• 出版时间：February 2010
• 年：2010
• 卷：117
• 期：2
• 页码：189-195
• 全文大小：201 K

文摘

In this note we establish a Ramsey-type result for certain subsets of the n-dimensional cube. This can then be applied to obtain reasonable bounds on various related structures, such as (partial) Hales–Jewett lines for alphabets of sizes 3 and 4, Hilbert cubes in sets of real numbers with small sumsets, “corners” in the integer lattice in the plane, and 3-term integer geometric progressions.