Sums in the grid

DOI10.1016/S0012-365X(96)00303-2zbMath0872.11007OpenAlexW2030028746MaRDI QIDQ1356653

Imre Leader, Béla Bollobás

Publication date: 7 July 1997

Published in: Discrete Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0012-365x(96)00303-2

zbMATH Keywords

lower boundsaddition of sets

Mathematics Subject Classification ID

Permutations, words, matrices (05A05) Density, gaps, topology (11B05)

Related Items (23)

On Sums of Generating Sets in ℤ₂ⁿ ⋮ The Brunn-Minkowski inequality ⋮ A bound on partitioning clusters ⋮ Parity and strong parity edge-colorings of graphs ⋮ Partitions of nonzero elements of a finite field into pairs ⋮ Sets in \(\mathbb{Z}^k\) with doubling \(2^k + \delta\) are near convex progressions ⋮ Optimally small sumsets in finite abelian groups. ⋮ Explicit constructions of RIP matrices and related problems ⋮ BOUNDS ON THE MINIMAL SUMSET SIZE FUNCTION IN GROUPS ⋮ Inverse additive problems for Minkowski sumsets. I ⋮ The Freiman-Ruzsa theorem over finite fields ⋮ A Brunn-Minkowski inequality for the integer lattice ⋮ Freiman's Theorem in Finite Fields via Extremal Set Theory ⋮ Large values of the additive energy in and ⋮ Minimal sumsets in finite solvable groups. ⋮ Properties of two-dimensional sets with small sumset ⋮ Old and new formulas for the Hopf-Stiefel and related functions ⋮ Sums of finite subsets in \(\mathbb{R}^d\) ⋮ Sums of finite subsets in \(\mathbb{R}^d\) ⋮ THE ISOPERIMETRIC METHOD IN NON-ABELIAN GROUPS WITH AN APPLICATION TO OPTIMALLY SMALL SUMSETS ⋮ Optimal strong parity edge-coloring of complete graphs ⋮ The number of \(k\)-sums modulo \(k\) ⋮ Some extensions of the Cauchy-Davenport theorem

Cites Work

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• On the sum of two sets in a group
• Isoperimetric inequalities and fractional set systems
• Exact face-isoperimetric inequalities
• On small sumsets in an abelian group
• Edge-isoperimetric inequalities in the grid
• Abschätzung der asymptotischen Dichte von Summenmengen
• Reverse Kleitman Inequalities
• Discrete Isoperimetric Problems
• On the Addition of Residue Classes
• On Kneser's Addition Theorem in Groups
• A Historical Note
• A Theorem on the Densities of Sets of Integers

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