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JOURNAL OF COMBINATORIAL THEORY, Series A 41, 154-157 (1986) The Number of Small Semispaces
 

Summary: JOURNAL OF COMBINATORIAL THEORY, Series A 41, 154-157 (1986)
Note
The Number of Small Semispaces
of a Finite Set of Points in the Plane
N~CA ALON*
Department of Mathematics, Massachusetts Institute of Technology,
Cambridge, Massachusetts 02139
AND
E. GY~RI
Mathematical Institute of the Hungarian
Academy of Sciences, Budapest, Hungary
Communicated by the Managing Editors
Received May 22, 1984
For a configuration S of n points in the plane, let gk(S) denote the number of
subsets of cardinality man and Pollack (J. Combin. Theory Ser. A 36 (1984), 101-104) showed that if
k < n/2 then g,,, < 2nk - 2k2 -k. Here we show that g,," = k. n for k Academic Press, Inc.
Let S be a finite set of points in the plane. Following Goodman and
Pollack [GP2] we call the intersection of S with a half plane a semispace

  

Source: Alon, Noga - School of Mathematical Sciences, Tel Aviv University

 

Collections: Mathematics