Results 21 to 30 of about 51 (51)
Block sizes in the block sets conjecture
Forum of Mathematics, SigmaA 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 +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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Bohr Topologies and Partition Theorems for Vector Spaces
, 1997 We prove a Ramsey-style theorem for sequences of vectors in an infinite-dimensional vector space over a finite field. As an application of this theorem, we prove that there are countably infinite Abelian groups whose Bohr topologies are not homeomorphic.
Kenneth Kunen, Kunen, Kenneth
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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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Forum of Mathematics, SigmaA 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 +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, SigmaA 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 +7 more
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The weak Ramsey property and extreme amenability
Forum of Mathematics, SigmaWe 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 +3 more
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Forum of Mathematics, SigmaWe 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 +4 more
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Ramsey-Type Results for Oriented Trees
, 2007 . For a graph G and a digraph ~ H, we write G! ~ H (respectively, G a ! ~ H) if every orientation (respectively, acyclic orientation) of the edges of G results in an induced copy of ~ H. In this note we study how small the graphs G such that G!
Vojtech Rödl +2 more
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