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The unit distance problem for centrally symmetric convex Bernardo M. brego
 

Summary: The unit distance problem for centrally symmetric convex
polygons
Bernardo M. Ábrego
Department of Mathematics
California State University, Northridge
Silvia Fernández-Merchant
Department of Mathematics
California State University, Northridge
January 2002
Abstract
Let f(n) be the maximum number of unit distances determined by the vertices of a convex
n-gon. Erdos and Moser conjectured that this function is linear. Supporting this conjecture
we prove that fsym
(n) 2n where fsym
(n) is the restriction of f (n) to centrally symmetric
convex n-gons. We also present two applications of this result. Given a strictly convex domain
K with smooth boundary, if fK (n) denotes the maximum number of unit segments spanned by
n points in the boundary of K, then fK (n) = O (n) whenever K is centrally symmetric or has
width > 1.
1 Introduction

  

Source: Abrego, Bernardo - Department of Mathematics, California State University, Northridge
Fernandez, Silvia - Department of Mathematics, California State University, Northridge

 

Collections: Mathematics