منابع مشابه
Economical coverings of sets of lattice points
Let t(n, d) be the minimum number t such that there are t of the n lattice points {(x1, . . . , xd) : 1 ≤ xi ≤ n} so that the ( t 2 ) lines that they determine cover all the above n lattice points. We prove that for every integer d ≥ 2 there are two positive constants c1 = c1(d) and c2 = c2(d) such that for every n c1n d(d−1)/(2d−1) ≤ t(n, d) ≤ c2n log n. The special case d = 2 settles a proble...
متن کاملBisections of Two Sets of Points in the Plane Lattice
Assume that 2m red points and 2n blue points are given on the lattice Z2 in the plane R2. We show that if they are in general position, that is, if at most one point lies on each vertical line and horizontal line, then there exists a rectangular cut that bisects both red points and blue points. Moreover, if they are not in general position, namely if some vertical and horizontal lines may conta...
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ژورنال
عنوان ژورنال: Indagationes Mathematicae (Proceedings)
سال: 1958
ISSN: 1385-7258
DOI: 10.1016/s1385-7258(58)50028-6