Linear Sets with Five Distinct Differences among Any Four Elements

A. Gyárfás, J. Lehel

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

As a generalization of the concept of Sidon sets, a set of real numbers is called a (4, 5)-set if every four-element subset determines at least five distinct differences. Let g(n) be the largest number such that any n-element (4,5)-set contains a g(n)-element Sidon set (i.e., a subset of g(n) elements with distinct differences). It is shown that ( 1 2 + ε{lunate}) n ≤ g(n) ≤ 3n 5 + 1, where ε{lunate} is a positive constant. The main result is the lower bound whose proof is based on a Turán-type theorem obtained for sparse 3-uniform hypergraphs associated with (4, 5)-sets.

Original languageEnglish
Pages (from-to)108-118
Number of pages11
JournalJournal of Combinatorial Theory. Series B
Volume64
Issue number1
DOIs
Publication statusPublished - May 1995

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Sidon Sets
Distinct
Subset
Uniform Hypergraph
Lower bound
Theorem

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Cite this

Linear Sets with Five Distinct Differences among Any Four Elements. / Gyárfás, A.; Lehel, J.

In: Journal of Combinatorial Theory. Series B, Vol. 64, No. 1, 05.1995, p. 108-118.

Research output: Contribution to journalArticle

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