On a problem involving unit fractions

2024/03/25 by Stefan Steinerberger, Steinerberger, Stefan
Mathematics · #Combinatorics (math.CO) #Differential Equations and Boundary Problems #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.2403.17041

openalex publication_date 2024/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Erdős and Graham proposed to determine the number of subsets S ⊆ \1,2,…,n\ with ∑_{s ∈ S} 1/s = 1 and asked, among other things, whether that number could be as large as 2^{n - o(n)}. We show that the number of subsets S ⊆ \1,2,…,n\ with ∑_{s ∈ S} 1/s ≤ 1 is smaller than 2^0.93n.

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