TY - JOUR
T1 - The number of small semispaces of a finite set of points in the plane
AU - Alon, Noga
AU - Györi, E.
PY - 1986/1
Y1 - 1986/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=38249043947&partnerID=8YFLogxK
U2 - 10.1016/0097-3165(86)90122-6
DO - 10.1016/0097-3165(86)90122-6
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AN - SCOPUS:38249043947
SN - 0097-3165
VL - 41
SP - 154
EP - 157
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
IS - 1
ER -