Ramsey monoids
Abstract
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 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 Sch\"utzenberger's theorem and finite automata theory.
Cite
@article{arxiv.2012.02506,
title = {Ramsey monoids},
author = {Claudio Agostini and Eugenio Colla},
journal= {arXiv preprint arXiv:2012.02506},
year = {2021}
}
Comments
The structure of the paper has been strongly reworked, and some sections have been removed, accordingly to the referee's suggestions. Added new results on Solecki's generalization of Furstenberg and Katznelson's theorem. Added references for aperiodic monoids