The number of Sidon sets and the maximum size of Sidon sets contained in a sparse random set of integers

DOI10.1002/rsa.20496zbMath1402.11021OpenAlexW1994460676WikidataQ105583285 ScholiaQ105583285MaRDI QIDQ5175228

Yoshiharu Kohayakawa, Wojciech Samotij, Vojtěch Rödl, Sang June Lee

Publication date: 20 February 2015

Published in: Random Structures & Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/rsa.20496

zbMATH Keywords

Sidon setsadditive combinatoricsrandom sets of integersprobabilistic extremal problems

Mathematics Subject Classification ID

Other combinatorial number theory (11B75) Additive bases, including sumsets (11B13) Probabilistic methods in extremal combinatorics, including polynomial methods (combinatorial Nullstellensatz, etc.) (05D40) Arithmetic combinatorics; higher degree uniformity (11B30)

Related Items (23)

The number of \(B_3\)-sets of a given cardinality ⋮ The number of \(C_{2\ell}\)-free graphs ⋮ Online containers for hypergraphs, with applications to linear equations ⋮ On solution-free sets of integers ⋮ Deviation probabilities for arithmetic progressions and other regular discrete structures ⋮ The number of multiplicative Sidon sets of integers ⋮ The asymptotics of \(r(4,t)\) ⋮ Infinite Sidon Sets Contained in Sparse Random Sets of Integers ⋮ On the Number ofB_h-Sets ⋮ Erdős–Ko–Rado for Random Hypergraphs: Asymptotics and Stability ⋮ Threshold functions and Poisson convergence for systems of equations in random sets ⋮ The counting version of a problem of Erdős ⋮ Hypergraph containers ⋮ Enumerating solution-free sets in the integers ⋮ Turán numbers for Berge-hypergraphs and related extremal problems ⋮ Intersecting families of discrete structures are typically trivial ⋮ Counting sum-free sets in abelian groups ⋮ Random sum-free subsets of abelian groups ⋮ Finding large co-Sidon subsets in sets with a given additive energy ⋮ On strong infinite Sidon and \(B_h\) sets and random sets of integers ⋮ On the number of generalized Sidon sets ⋮ On the independence number of non-uniform uncrowded hypergraphs ⋮ Counting independent sets in graphs

Cites Work

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• Linear problems in combinatorial number theory
• Szemerédi’s Regularity Lemma for Sparse Graphs
• On uncrowded hypergraphs
• Arithmetic progressions of length three in subsets of a random set
• The number of K _s,t -free graphs
• On Certain Sets of Integers
• On a Problem of Sidon in Additive Number Theory, and on some Related Problems
• On a Problem of Sidon in Additive Number Theory and on Some Related Problems Addendum
• Concentration of multivariate polynomials and its applications

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