Caps and progression-free sets in \(\mathbb{Z}_m^n\)
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Publication:2004972
DOI10.1007/s10623-020-00769-0zbMath1465.11051arXiv1903.08266OpenAlexW3036512481WikidataQ100725716 ScholiaQ100725716MaRDI QIDQ2004972
Péter Pál Pach, Christian Elsholtz
Publication date: 7 October 2020
Published in: Designs, Codes and Cryptography (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1903.08266
Cryptography (94A60) Finite abelian groups (20K01) Linear codes and caps in Galois spaces (51E22) Arithmetic progressions (11B25)
Related Items (6)
Bounds on the size of progression-free sets in \(\mathbb{Z}_m^n\) ⋮ Sets Avoiding Six-Term Arithmetic Progressions in $\mathbb{Z}_6^{n}$ are Exponentially Small ⋮ Improved bounds for progression-free sets in \(C_8^n\) ⋮ Finding solutions with distinct variables to systems of linear equations over \(\mathbb{F}_p\) ⋮ Exponentially larger affine and projective caps ⋮ Large subsets of \(\mathbb{Z}_m^n\) without arithmetic progressions
Cites Work
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- On sunflowers and matrix multiplication
- Progression-free sets in \(\mathbb{Z}_4^n\) are exponentially small
- On large subsets of \(\mathbb{F}_q^n\) with no three-term arithmetic progression
- Lower bounds for multidimensional zero sums
- On Roth's theorem on progressions
- Roth's theorem in \(\mathbb Z^n_4\)
- Matrix multiplication via arithmetic progressions
- On subsets of \(\mathbb F_q^n\) containing no \(k\)-term progressions
- Maximal caps in \(\mathrm{AG}(6,3)\).
- Sequences in abelian groups \(G\) of odd order without zero-sum subsequences of length \(\exp(G)\)
- On subsets of abelian groups with no 3-term arithmetic progression
- A density version of a geometric Ramsey theorem
- Maximal three-independent subsets of \(\{0,1,2\}^ n\)
- The card game SET.
- Progression-free sets in finite abelian groups.
- Extensions of generalized product caps
- An improved construction of progression-free sets
- The classification of the largest caps in AG(5, 3)
- On subsets of finite Abelian groups with no 3-term arithmetic progressions
- A lattice point problem and additive number theory
- On triples in arithmetic progression
- Exponential bounds for the Erdős-Ginzburg-Ziv constant
- Improved bounds for progression-free sets in \(C_8^n\)
- On Kemnitz' conjecture concerning lattice-points in the plane
- Edmonds polytopes and a hierarchy of combinatorial problems. (Reprint)
- Finite field models in arithmetic combinatorics -- ten years on
- New bounds on cap sets
- Density Hales-Jewett and Moser numbers
- ZERO-SUM PROBLEMS IN FINITE ABELIAN GROUPS AND AFFINE CAPS
- New bounds for Szemerédi's theorem, I: progressions of length 4 in finite field geometries
- Regularity and Positional Games
- On sets of integers containing k elements in arithmetic progression
- On cap sets and the group-theoretic approach to matrix multiplication
- On the Solution of Moser's Problem in Four Dimensions
- A new exponential upper bound for the Erd\H{o}s-Ginzburg-Ziv constant
- Maximal sum-free sets of integer lattice grids
- Multiplying matrices faster than coppersmith-winograd
- The Minimal Number of Three-Term Arithmetic Progressions Modulo a Prime Converges to a Limit
- A Lattice Point Problem Related to Sets Containing No l-Term Arithmetic Progression
- Remarks on a Problem of Moser
- On Certain Sets of Integers
- On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
- On Sets of Integers Which Contain No Three Terms in Arithmetical Progression
- Large caps in small spaces
- A new proof of Szemerédi's theorem
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