Results 21 to 30 of about 52 (52)

MONOID ACTIONS AND ULTRAFILTER METHODS IN RAMSEY THEORY

Forum of Mathematics, Sigma, 2019
First, we prove a theorem on dynamics of actions of monoids by endomorphisms of semigroups. Second, we introduce algebraic structures suitable for formalizing infinitary Ramsey statements and prove a theorem that such statements are implied by the ...
SŁAWOMIR SOLECKI
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Density of monochromatic infinite subgraphs II

Forum of Mathematics, Sigma
In 1967, Gerencsér and Gyárfás [16] proved a result which is considered the starting point of graph-Ramsey theory: In every 2-coloring of $K_n$ , there is a monochromatic path on $\lceil (2n+1)/3\rceil $ vertices, and this is best possible ...
Jan Corsten, Louis DeBiasio, Paul McKenney   +2 more
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Block sizes in the block sets conjecture

Forum of Mathematics, Sigma
A set X is called Euclidean Ramsey if, for any k and sufficiently large n, every k-colouring of $\mathbb {R}^n$ contains a monochromatic congruent copy of X.
Maria-Romina Ivan, Imre Leader, Mark Walters   +2 more
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On the Vertex Folkman Numbers Fv(2,...,2;q) [PDF]

, 2009
2000 Mathematics Subject Classification: 05C55.In this paper we shall compute the Folkman numbers ...
Nenov, Nedyalko
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New Upper Bound for the Edge Folkman Number Fe(3,5;13) [PDF]

, 2008
2000 Mathematics Subject Classification: 05C55.For a given graph G let V(G) and E(G) denote the vertex and the edge set of G respevtively. The symbol G e → (a1, …, ar) means that in every r-coloring of E(G) there exists a monochromatic ai-clique of ...
Kolev, Nikolay
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The power of many colours

Forum of Mathematics, Sigma
A classical problem, due to Gerencsér and Gyárfás from 1967, asks how large a monochromatic connected component can we guarantee in any r-edge colouring of $K_n$ ?
Noga Alon, Matija Bucić, Micha Christoph, Michael Krivelevich   +3 more
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Variations of classical selection principles: an overview

, 2020
The paper is an overview of selected results on weaker forms of classical selection principles of Menger, Hurewicz, Rothberger and Gerlits-Nagy obtained in the last few years.
Kočinac, Ljubiša D.R.
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Topological methods in zero-sum Ramsey theory

Forum of Mathematics, Sigma
A landmark result of Erdős, Ginzburg, and Ziv (EGZ) states that any sequence of $2n-1$ elements in ${\mathbb {Z}}/n$ contains a zero-sum subsequence of length n.
Florian Frick, Jacob Lehmann Duke, Meenakshi McNamara, Hannah Park-Kaufmann, Steven Raanes, Steven Simon, Darrion Thornburgh, Zoe Wellner   +7 more
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Echeloned Spaces

Forum of Mathematics, Sigma
We introduce the notion of echeloned spaces – an order-theoretic abstraction of metric spaces. The first step is to characterize metrizable echeloned spaces. It turns out that morphisms between metrizable echeloned spaces are uniformly continuous or have
Maxime Gheysens, Bojana Pavlica, Christian Pech, Maja Pech, Friedrich Martin Schneider   +4 more
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The weak Ramsey property and extreme amenability

Forum of Mathematics, Sigma
We extend the Kechris–Pestov–Todorčević correspondence to weak Fraïssé categories and automorphism groups of generic objects. The new ingredient is the weak Ramsey property.
Adam Bartoš, Tristan Bice, Keegan Dasilva Barbosa, Wiesław Kubiś   +3 more
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