Partition regular structures contained in large sets are abundant

DOI10.1006/jcta.2000.3061zbMath0966.05078OpenAlexW1999929451MaRDI QIDQ5929833

Vitaly Bergelson, Neil Hindman

Publication date: 12 August 2001

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/df66006358bc325c91e5df09d94e7059fdbb9c24

zbMATH Keywords

semigroupsarithmetic progressionHales-Jewett theorempartition regular structuresRamsey theory

Mathematics Subject Classification ID

Ramsey theory (05D10) Arithmetic progressions (11B25)

Related Items (26)

A combinatorial viewpoint on preserving notion of largeness and an abstract Rado theorem ⋮ Multiplicative richness of additively large sets in \(\mathbb{Z}^d\) ⋮ Multiplicative structures in additively large sets ⋮ Chain transitivity and variations of the shadowing property ⋮ On Rado conditions for nonlinear Diophantine equations ⋮ Down the large rabbit hole ⋮ Large sets near idempotent and its product ⋮ Idempotent ultrafilters without Zorn’s Lemma ⋮ Some dynamical properties related to polynomials ⋮ Abundance of progressions in a commutative semigroup by elementary means ⋮ Unnamed Item ⋮ Mixing via the extended family ⋮ Unnamed Item ⋮ Translation Invariant Filters and van der Waerden’s Theorem ⋮ Largeness of the set of finite products in a semigroup ⋮ The relationships among many notions of largeness for subsets of a semigroup ⋮ Richness of arithmetic progression in commutative semigroup ⋮ Large sets in Boolean and non-Boolean groups and topology ⋮ A history of central sets ⋮ Unnamed Item ⋮ Notions of size in a semigroup: an update from a historical perspective ⋮ On the interplay between additive and multiplicative largeness and its combinatorial applications ⋮ Iterated differences sets, Diophantine approximations and applications ⋮ Arithmetic progressions in abundance by combinatorial tools ⋮ The research of thirteen students at Howard university ⋮ Quotient sets and density recurrent sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite union theorem with restrictions
• Restricted Ramsey configurations
• Algebra in the Stone-Čech compactification: theory and applications
• An interesting combinatorial method in the theory of locally finite semigroups
• Ramsey's theorem for a class of categories
• Sets Partition Regular for n Equations Need not Solve n + 1
• Regularity and Positional Games
• Divisible Properties and the Stone-Čech Compactification
• Compact subsemigroups of (βℕ, +) containing the idempotents
• Polynomial extensions of van der Waerden’s and Szemerédi’s theorems

This page was built for publication: Partition regular structures contained in large sets are abundant