A note on the Erdős conjecture about square packing

2024/11/11 by Baek, Jineon, Koizumi, Junnosuke, Ueoro, Takahiro
#52C10 #52C15 #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2411.07274

Abstract

Let f(n) denote the maximum total length of the sides of n squares packed inside a unit square. Erdős conjectured that f(k²+1)=k. We show that the conjecture is true if we assume that the sides of the squares are parallel to the sides of the unit square.

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