论文标题
不一致的集和崇高的拉姆齐理论
Discordant sets and ergodic Ramsey theory
论文作者
论文摘要
我们探讨了具有正密度的非彩态联合集合的性质，我们称之为“不和谐”，在无数的无限木（半）组中。这种集合涉及拉姆西理论的许多问题，并表现出古典范德沃登定理和szemerédi定理之间复杂性的差异。我们概括并统一旧结构，并获得有关这些历史上有趣的集合的新结果。一路上，我们从数学的各个角落中汲取灵感，包括经典的拉姆西理论，厄基德理论，数字理论以及拓扑和象征动力学。
We explore the properties of non-piecewise syndetic sets with positive upper density, which we call "discordant", in countably infinite amenable (semi)groups. Sets of this kind are involved in many questions of Ramsey theory and manifest the difference in complexity between the classical van der Waerden's theorem and Szemerédi's theorem. We generalize and unify old constructions and obtain new results about these historically interesting sets. Along the way, we draw from various corners of mathematics, including classical Ramsey theory, ergodic theory, number theory, and topological and symbolic dynamics.
