Point-sets in General Position with Many Similar Copies of a Pattern
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چکیده
For every pattern P , consisting of a finite set of points in the plane, S′ P (n) is defined as the largest number of similar copies of P among sets of n points in the plane without 3 points on a line. A general construction, based on iterated Minkovski sums, is used to obtain new lower bounds for S′ P (n) when P is an arbitrary pattern. Improved bounds are obtained when P is a triangle or a regular polygon with few sides.
منابع مشابه
Point-sets with Many Similar Copies of a Pattern: without a Fixed Number of Collinear Points or in Parallelogram-free Position
Let P be a finite pattern, that is, a finite set of points in the plane. We consider the problem of maximizing the number of similar copies of P over all sets of n points in the plane under two general position restrictions: (1) Over all sets of n points with no m points on a line. We call this maximum SP (n,m). (2) Over all sets of n points with no collinear triples and not containing the 4 ve...
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For every pattern P , consisting of a finite set of points in the plane, SP (n,m) is defined as the largest number of similar copies of P among sets of n points in the plane without m points on a line. A general construction, based on iterated Minkovski sums, is used to obtain new lower bounds for SP (n,m) when P is an arbitrary pattern. Improved bounds are obtained when P is a triangle or a re...
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تاریخ انتشار 2009