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Ramsey monoids
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Recently, Solecki [Forum Math. Sigma 7 (2019), p. 40] introduced the notion of Ramsey monoid to produce a common generalization to theorems such as Hindman’s theorem, Carlson’s theorem, and Gowers’
F
I
N
k
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.
American Mathematical Society (AMS)
Title: Ramsey monoids
Description:
Recently, Solecki [Forum Math.
Sigma 7 (2019), p.
40] introduced the notion of Ramsey monoid to produce a common generalization to theorems such as Hindman’s theorem, Carlson’s theorem, and Gowers’
F
I
N
k
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.
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