An Improvement of the Upper Bound for the Number of Halving Lines of Planar Sets-Reference-Cited by-同舟云学术

An Improvement of the Upper Bound for the Number of Halving Lines of Planar Sets

Published:2024-07-22 Issue:7 Volume:16 Page:936
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Alonso Estrella¹^ORCID,López Mariló²^ORCID,Rodrigo Javier¹^ORCID

Affiliation:

1. Department of Applied Mathematics, Technical School of Engineering, Comillas Pontifical University, Calle de Alberto Aguilera 25, 28015 Madrid, Spain

2. Department of Mathematics and Computer Science Applied to Civil Engineering, Polytechnic University of Madrid, Calle del Profesor Aranguren 3, 28040 Madrid, Spain

Abstract

In this paper, we provide improvements in the additive constant of the current best asymptotic upper bound for the maximum number of halving lines for planar sets of n points, where n is an even number. We also improve this current best upper bound for small values of n, namely, 106≤n≤336. To obtain this enhancements, we provide lower bounds for the sum of the squares of the degrees of the vertices of a graph related to the halving lines.

Funder

Ministerio de Economía y Competitividad of Spain

Agencia Estatal de Investigación (AEI), Ministerio de Ciencia e Innovación of Spain

Publisher

MDPI AG

Link

https://www.mdpi.com/2073-8994/16/7/936/pdf

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