Generalized sum-free subsets

Yair Caro

International Journal of Mathematics and Mathematical Sciences, 1990, vol. 13, 1-4

Abstract:

Let F = { A ( i ) : 1 ≤ i ≤ t , t ≥ 2 }, be a finite collection of finite, pairwise disjoint subsets of Z + . Let S ⊂ R \ { 0 } and A ⊂ Z + be finite sets. Denote by S A = { ∑ i = 1 a s i : a ∈ A , S i ∈ S , the s i are not necessarily distinct}. For S and F as above we say that S is F -free if for every A ( i ) , A ( j ) ∈ F , i ≠ j , S A ( i ) ⋂ S A ( j ) = ϕ .

We prove that for S and F as above, S contains an F -free subset Q such that | Q | ≥ c ( F ) | S | , when c ( F ) is a positive constant depending only on F .

This result generalizes earlier results of Erdos [3] and Alon and Kleitman [2], on sum-free subsets. Several possible extensions are also discussed.

Date: 1990
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/13/191240.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/13/191240.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:191240

DOI: 10.1155/S016117129000103X

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().