Related papers: Ramsey theory for layered semigroups

Let G be an unramified reductive group over a non archimedian local field F. The so-called "Langlands Fundamental Lemma" is a family of conjectural identities between orbital integrals for G(F) and orbital integrals for endoscopic groups of…

The purpose of this survey is to provide a gentle introduction to several recent breakthroughs in graph Ramsey theory. In particular, we will outline the proofs (due to various groups of authors) of exponential improvements to the diagonal,…

This article is concerned with classes of relational structures that are closed under taking substructures and isomorphism, that have the joint embedding property, and that furthermore have the Ramsey property, a strong combinatorial…

We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in terms of certain ultrafilters related to tensor products…

In this paper we provide purely categorical proofs of two important results of structural Ramsey theory: the result of M.\ Soki\'c that the free product of Ramsey classes is a Ramsey class and the result of M.\ Bodirsky, M.\Pinsker and T.\…

This paper is the fourth and the last part of the series "Spherical higher order Fourier analysis over finite fields", aiming to develop the higher order Fourier analysis method along spheres over finite fields, and to solve the Geometric…

For a given graph $F$ we consider the family of (finite) graphs $G$ with the Ramsey property for $F$, that is the set of such graphs $G$ with the property that every two-colouring of the edges of $G$ yields a monochromatic copy of $F$. For…

We provide two new proofs of the infinitude of prime numbers, using the additive Ramsey-theoretic result known as Folkman's theorem (alternatively, one can think of these proofs as using Hindman's theorem). This adds to the existing…

This paper has two parts. First, we complete the proof of the Kolmogorov extension theorem for unbounded random variables using compactness theorem of integral logic which was proved for bounded case in [8]. Second, we give a proof of the…

We detect topological semigroups that are topological paragroups, i.e., are isomorphic to a Rees product of a topological group over topological spaces with a continuous sandwich function. We prove that a simple topological semigroup $S$ is…

We show a general scheme of Ramsey-type results for partitions of countable sets of finite functions, where "one piece is big" is interpreted in the language originating in creature forcing. The heart of our proofs follows Glazer's proof of…

We develop a general framework for infinite-dimensional Ramsey theory with and without pigeonhole principle, inspired by Gowers' Ramsey-type theorem for block sequences in Banach spaces and by its exact version proved by Rosendal. In this…

The (.)_reg construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)_reg which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J-order structure). We show…

We show that every free amalgamation class of finite structures with relations and (symmetric) partial functions is a Ramsey class when enriched by a free linear ordering of vertices. This is a common strengthening of the…

One way of studying a relational structure is to investigate functions which are related to that structure and which leave certain aspects of the structure invariant. Examples are the automorphism group, the self-embedding monoid, the…

In this note we consider a Ramsey type result for partially ordered sets. In particular, we give an alternative short proof of a theorem for a posets with multiple linear extensions recently obtained by Solecki and Zhao.

A sequence $s_1,s_2,\ldots, s_k$ of elements of a group $G$ is called a valid ordering if the partial products $s_1, s_1 s_2, \ldots, s_1\cdots s_k$ are all distinct. A long-standing problem in combinatorial group theory asks whether, for a…

In this article, we investigate homogeneous versions of certain nonlinear Ramsey-theoretic results, with three significant applications. As the first application, we prove that for every finite coloring of $\mathbb{Z}^+$, there exist an…

We prove a generalized version of the Morse index theorem for geodesics endowed with a non positive definite metric tensor (semi-Riemannian manifolds). We apply the result to obtain lower estimates on the number of geodesics joining two…

Chudnovsky, Kim, Oum, and Seymour recently established that any prime graph contains one of a short list of induced prime subgraphs [1]. In the present paper we reprove their theorem using many of the same ideas, but with the key…