A density statement generalizing Schur's theorem

DOI10.1016/0097-3165(86)90074-9zbMath0607.10040OpenAlexW2052945128MaRDI QIDQ1085206

Vitaly Bergelson

Publication date: 1986

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

Full work available at URL: https://doi.org/10.1016/0097-3165(86)90074-9

zbMATH Keywords

Schur theoremupper asymptotic densityFurstenberg's method

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Density, gaps, topology (11B05)

Related Items (11)

On \(\text{IP}^*\) sets and central sets ⋮ Density versions of two generalizations of Schur's theorem ⋮ A combinatorially large cell of a partition of N ⋮ Additive and Multiplicative Ramsey Theorems in ℕ – Some Elementary Results ⋮ Density in locally compact topological groups ⋮ Ergodic theorem involving additive and multiplicative groups of a field and patterns ⋮ Uniform distribution of prime powers and sets of recurrence and van der Corput sets in \(\mathbb{Z}^k\) ⋮ On monochromatic solutions to \(x-y=z^2\) ⋮ Density versions of Schur's theorem for ideals generated by submeasures ⋮ Iterated combinatorial density theorems ⋮ A selection of open problems

Cites Work

• An ergodic Szemerédi theorem for IP-systems and combinatorial theory
• An ergodic Szemerédi theorem for commuting transformations
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Sets of Recurrence of Z^m -Actions and Properties of Sets of Differences in Z^m
• Note on a Property of Measurable Sets
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