The number of small semispaces of a finite set of points in the plane

Noga Alon*, E. Györi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

For a configuration S of n points in the plane, let gk(S) denote the number of subsets of cardinality ≤k cut off by a line. Let gk,n = max{gk(S): |S| = n}. Goodman and Pollack (J. Combin. Theory Ser. A 36 (1984), 101-104) showed that if k < n 2 then gk,n ≤ 2nk - 2k2 - k. Here we show that gk,n = k·n for k < n 2.

Original languageEnglish
Pages (from-to)154-157
Number of pages4
JournalJournal of Combinatorial Theory. Series A
Volume41
Issue number1
DOIs
StatePublished - Jan 1986
Externally publishedYes

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