论文标题
拉姆西单人
Ramsey monoids
论文作者
论文摘要
最近，Solecki介绍了Ramsey Monoid的概念，以对Hindman定理，Carlson的定理和Gowers的Fin $ _K $定理产生共同的概括。他证明了整个有限的单体都是拉姆西。在这里，我们改善了这一结果，扩大了该类别，并找到了有限的Ramsey Monoids的简单代数表征。我们以相似的方式扩展了Solecki的结果，该结果是第二类与Furstenberg-Katznelson Ramsey Theorem相连的单体。获得的结果表明，可能与Schützenberger定理和有限自动机理论建立联系。
Recently, Solecki introduced the notion of Ramsey monoid to produce a common generalization to theorems such as Hindman's theorem, Carlson's theorem, and Gowers' FIN$_k$ theorem. He proved that an entire class of finite monoids is Ramsey. Here we improve this result, enlarging this class and finding a simple algebraic characterization of finite Ramsey monoids. We extend in a similar way a result of Solecki regarding a second class of monoids connected to the Furstenberg-Katznelson Ramsey Theorem. The results obtained suggest a possible connection with Schützenberger's theorem and finite automata theory.
