Disjoint Empty Convex Pentagons in Planar Point Sets
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Statistics Papers
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convex hull
discrete geometry
empty convex polygons
Erdős-Szekeres theorem
pentagons
Applied Mathematics
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Mathematics
Statistics and Probability
discrete geometry
empty convex polygons
Erdős-Szekeres theorem
pentagons
Applied Mathematics
Business
Mathematics
Statistics and Probability
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Bhattacharya, Bhaswar B
Das, Sandip
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Abstract
In this paper we obtain the first non-trivial lower bound on the number of disjoint empty convex pentagons in planar points sets. We show that the number of disjoint empty convex pentagons in any set of n points in the plane, no three on a line, is at least ā5n/47ā. This bound can be further improved to (3nā1)/28 for infinitely many n.
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2016-03-01