Statistics Papers

Document Type

Technical Report

Date of this Version

3-2016

Publication Source

Periodica Mathematica Hungaria

Volume

66

Issue

1

Start Page

73

Last Page

86

DOI

10.1007/s10998-013-9078-z

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 ⌊5n/47⌋. This bound can be further improved to (3n−1)/28 for infinitely many n.

Copyright/Permission Statement

This is a pre-print of an article published in Periodica Mathematica Hungaria. The final authenticated version is available online at: http://dx.doi.org/10.1007/s10998-013-9078-z

Keywords

convex hull, discrete geometry, empty convex polygons, Erdős-Szekeres theorem, pentagons

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Date Posted: 25 October 2018

This document has been peer reviewed.