On density, translates, and pairwise sums of integers

DOI10.1016/0097-3165(82)90003-6zbMath0496.10036OpenAlexW2082471372MaRDI QIDQ1170286

Neil Hindman

Publication date: 1982

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(82)90003-6

zbMATH Keywords

asymptotic densitytranslates of setsupper densitypairwise sumspositive-maximal density

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Special sequences and polynomials (11B83) Arithmetic progressions (11B25)

Related Items (10)

An ergodic correspondence principle, invariant means and applications ⋮ Filters and the Weak Almost Periodic Compactification of a Discrete Semigroup ⋮ Some equivalents of the Erdős sum of reciprocals conjecture ⋮ Subprincipal closed ideals in \(\beta N\) ⋮ Multiple recurrence and popular differences for polynomial patterns in rings of integers ⋮ On creating sets with large lower density ⋮ A proof of a sumset conjecture of Erdős ⋮ On some generalizations of Lorentz's almost convergence ⋮ Sumset phenomenon in countable amenable groups ⋮ High density piecewise syndeticity of sumsets

Cites Work

• Sums equal to products in \(\beta{\mathbb N}\)
• Sumsets contained in infinite sets of integers
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Finite sums from sequences within cells of a partition of N
• On sets of integers containing k elements in arithmetic progression
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