Ramsey monoids

Claudio Agostini, Eugenio Colla

Published 2020-12-04Version 1

Recently, Solecki introduced the notion of Ramsey monoid to produce a common generalization to famous 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 also extend in a similar manner a theorem of Solecki that, in turn, generalizes one of Furstenberg and Katznelson. Finally, we show how in this context partition theorems for located words can be derived from partition theorems for words.