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Algebra in the Stone-Cech Compactification: Theory and Applications
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a largeExpand
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Finite Sums from Sequences Within Cells of a Partition of N
  • N. Hindman
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. A
  • 1 July 1974
TLDR
We prove the validity of a conjecture by Graham and Rothschild that, if the natural numbers are divided into two classes, there is a sequence drawn from one of those classes such that all finite sums of distinct members of that sequence remain in the same class. Expand
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Ramsey Theoretic Consequences of Some New Results About Algebra in the Stone-Čech Compactification
Recently [4] we have obtained some new algebraic results about βN, the Stone-Cech compactification of the discrete set of positive integers and about βW , where W is the free semigroup over aExpand
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Multiplicative structures in additively large sets
TLDR
We investigate whether a subset of N with bounded gaps--a syndetic set--must contain arbitrarily long geometric progressions and arbitrarily long arithmetic progressions. Expand
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Partition Theorems for Spaces of Variable Words
Furstenberg and Katznelson applied methods of topological dynamics to Ramsey theory, obtaining a density version of the Hales-Jewett partition theorem. Inspired by their methods, but using spaces ofExpand
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Nonmetrizable topological dynamics and Ramsey theory
Applying ideas from topological dynamics in compact metric spaces to the Stone-Cech compactification of a discrete semigroup, several new proofs of old results and some new results in Ramsey TheoryExpand
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On strongly summable ultrafilters and union ultrafilters
We prove that union ultrafilters are essentially the same as strongly summable ultrafilters but ordered-union ultrafilters are not. We also prove that the existence of ultrafilters of these sortsExpand
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Open Problems in Partition Regularity
TLDR
A finite or infinite matrix A with rational entries is called partition regular if, whenever the natural numbers are finitely coloured, there is a monochromatic vector x with . Expand
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Density in Arbitrary Semigroups
We introduce some notions of density in an arbitrary semigroup S which extend the usual notions in countable left amenable semigroups in which density is based on Folner sequences. The new notionsExpand
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Monochromatic Sums Equal to Products in ℕ
Abstract Csikvári, Gyarmati, and Sárközy asked whether, whenever the set ℕ of positive integers is finitely colored, there must exist monochromatic a, b, c, and d with a ≠ b such that a + b = cd. WeExpand
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