Actions of trees on semigroups, and an infinitary Gowers--Hales--Jewett Ramsey theorem

2016/11/19 by Martino Lupini, Lupini, Martino
Computer Science · Mathematics · #05C05 #05D10 #06A06 (Secondary) #54D80 (Primary) 20M99 #Advanced Graph Theory Research #Advanced Topology and Set Theory #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.1611.06312

openalex publication_date 2016/11/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of (Ramsey) action of a tree on a (filtered) semigroup. We then prove in this setting a general result providing a common generalization of the infinitary Gowers Ramsey theorem for multiple tetris operations, the infinitary Hales--Jewett theorems (for both located and nonlocated words), and the Farah--Hindman--McLeod Ramsey theorem for layered actions on partial semigroups. We also establish a polynomial version of our main result, recovering the polynomial Milliken--Taylor theorem of Bergelson--Hindman--Williams as a particular case. We present applications of our Ramsey-theoretic results to the structure of delta sets in amenable groups.

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