On the interplay between additive and multiplicative largeness and its combinatorial applications
From MaRDI portal
Publication:2299645
DOI10.1016/j.jcta.2019.105203zbMath1433.05313arXiv1610.09771OpenAlexW2998772262WikidataQ126378181 ScholiaQ126378181MaRDI QIDQ2299645
Daniel Glasscock, Vitaly Bergelson
Publication date: 21 February 2020
Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1610.09771
central setsVan der WaerdenIP setspiecewise syndetic setsadditive and multiplicative upper Banach densitycombinatorial configurations in dense subsets of semigroupsHales-Jewett-type theoremsSzemerédi
Related Items (14)
A combinatorial viewpoint on preserving notion of largeness and an abstract Rado theorem ⋮ An ergodic correspondence principle, invariant means and applications ⋮ IP*-sets in function field and mixing properties ⋮ Combinatorially rich sets in arbitrary semigroups ⋮ Various recurrence and topologically sensitive for semiflows ⋮ Monochromatic quotients, products and polynomial sums in the rationals ⋮ Unnamed Item ⋮ Richness of arithmetic progression in commutative semigroup ⋮ Rado's criterion over squares and higher powers ⋮ Geometric progressions in syndetic sets ⋮ Image partition regular matrices and concepts of largeness ⋮ Monochromatic sums equal to products near zero ⋮ Central sets theorem along filters and some combinatorial consequences ⋮ On Katznelson’s Question for skew-product systems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Polynomial recurrence with large intersection over countable fields
- New polynomial and multidimensional extensions of classical partition results
- The shifted primes and the multidimensional Szemerédi and polynomial Van der Waerden theorems
- Algebra in the Stone-Čech compactification. Theory and applications
- On some arithmetical functions
- Multiplicatively large sets and ergodic Ramsey theory
- Multiplicative structures in additively large sets
- Density in arbitrary semigroups
- Density and invariant means in left amenable semigroups
- An ergodic Szemerédi theorem for IP-systems and combinatorial theory
- Topological dynamics and combinatorial number theory
- Representations of algebraic integers by binary quadratic forms and norm forms from full modules of extension fields
- On \(\text{IP}^*\) sets and central sets
- Multiplicative richness of additively large sets in \(\mathbb{Z}^d\)
- Revisiting the nilpotent polynomial Hales-Jewett theorem
- A density version of the Hales-Jewett theorem
- Set-polynomials and polynomial extension of the Hales-Jewett theorem
- Studien zur Kombinatorik
- Finite sums from sequences within cells of a partition of N
- Topological multiple recurrence for polynomial configurations in nilpotent groups
- Central sets and their combinatorial characterization
- The primes contain arbitrarily long arithmetic progressions
- On a Property of Non Liouville Numbers
- Ergodic theorem involving additive and multiplicative groups of a field and patterns
- Patterns and complexity of multiplicative functions
- 𝐼𝑃_𝑟-sets, Szemerédi’s theorem, and Ramsey theory
- Regularity and Positional Games
- Weyl Sums and Diophantine Approximation
- On sets of integers containing k elements in arithmetic progression
- Partitions and Sums and Products of Integers
- Additive and Multiplicative Ramsey Theorems in ℕ – Some Elementary Results
- Measure preserving actions of affine semigroups and patterns
- Pointwise convergence of ergodic averages for polynomial sequences of translations on a nilmanifold
- Nonmetrizable Topological Dynamics and Ramsey Theory
- Semigroups Satisfying a Strong Folner Condition
- The Structure of Distal Flows
- Polynomial extensions of van der Waerden’s and Szemerédi’s theorems
- Recurrence, rigidity, and popular differences
- Number fields
- Partition regular structures contained in large sets are abundant
- Finite products sets and minimally almost periodic groups
This page was built for publication: On the interplay between additive and multiplicative largeness and its combinatorial applications
