The Erdos and Campbell-Staton conjectures about square packing

2005/04/16 by Iwan Praton, Praton, Iwan
Engineering · Mathematics · #51M04 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Metric Geometry (math.MG) #graph theory and CDMA systems #math.MG #msc:51M04

paper · pdf · doi:10.48550/arxiv.math/0504341

2 pages

arxiv created 2005/04/16 · openalex publication_date 2005/04/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Put n open non-overlapping squares inside a unit square, and let f(n) denote the maximum possible value of the sum of the side lengths of the n squares. Campbell and Staton, building on a question of Erdos, conjectured that f(k²+2c+1)=k+c/k, where c is any integer and k≥ |c|. We show that if this conjecture is true for one value of c, then it is true for all values of c.

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