Sum Set Cardinalities of Line Restricted Planar Sets

Peter C. Fishburn
Additional contact information
Peter C. Fishburn: At&T Bell Laboratories

Chapter 9 in Number Theory: New York Seminar 1991–1995, 1996, pp 115-133 from Springer

Abstract: Abstract A theorem of G. Freiman says that if 2 ≤ λ 0 such that, for all finite sets X in the plane, if the sum set X+X has no more than λ|X| points then some line in the plane contains at least c|X| points of X. The present paper strengthens results used in Fishbum’s proof of Freiman’s theorem to obtain interestingly large values of c for which the theorem holds. For example, if the conclusion is to hold at least for suitably large |X|, then c=1 suffices for 2 ≤ X 1/k can give the desired result, even when |X| is restricted to be large.

Keywords: Line Segment; Convex Hull; Bell Laboratory; Preceding Inequality; Additive Number Theory (search for similar items in EconPapers)
Date: 1996
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

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:spr:sprchp:978-1-4612-2418-1_9

Ordering information: This item can be ordered from
http://www.springer.com/9781461224181

DOI: 10.1007/978-1-4612-2418-1_9

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().