Author(s): Dániel TÓTH

Title: SPECIÁLIS HALMAZOK ERDŐS–ULAM-SŰRŰSÉGE

Source: Š. Gubo, E. Kahler Korcsmáros, Sz. Svitek, J. Tóth (eds.): 17th International Scientific Conference of J. Selye University. Sessions of the Faculty of Economics and Informatics. Conference Proceedings

ISBN: 978-80-8122-538-3

DOI: https://doi.org/10.36007/5383.2026.359

Publisher: J. Selye University, Komárno, Slovakia

PY, pages: 2025, 359-365

Published on-line: 2026

Language: hu

Abstract: One of the most natural tools for measuring subsets of the natural numbers is the asymptotic density. The Erd˝os–Ulam density is a generalization of the asymptotic density. When studying such densities, we often work with sets of the form A = S∞ n=1 􀀀 (cn, dn] ∩ N , where the integer sequences (cn) and (dn) satisfy 0 ≤ cn < dn < cn+1. With the help of such block-structured sets, the properties of Erd˝os–Ulam densities can be investigated. In this paper, we apply the Cesàro– Stolz theorem to compute Erd˝os–Ulam densities. We determine some necessary and sufficient conditions for the existence of the Erd˝os–Ulam density. We also study the relationship between densities defined by the Erdős–Ulam functions f (n) and f ∗(n) = f (n)/( f (1) + · · · + f (n)) in the case of block-structured sets.

Keywords: asymptotic density, logarithmic density, Erdős–Ulam density

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