Creating subsets of natural numbers with a given weighted density

Tóth, Dániel (2025) Creating subsets of natural numbers with a given weighted density. DIMENZIÓK : MATEMATIKAI KÖZLEMÉNYEK (13). pp. 3-11. ISSN 2064-2172

Preview

Text dimenziok-13evf-2025-13k-003-011.pdf - Published Version Available under License Creative Commons Attribution Non-commercial Share Alike. Download (232kB) | Preview

Abstract

When studying the weighted densities of subsets of the natural numbers, we often work with block-structured sets of the form A = S∞ n=1 (cn, dn] ∩ N , where the integer sequences (cn) and (dn) satisfy 0 ≤ cn < dn < cn+1. In this article, we examine how to construct sets with arbitrary lower and upper weighted density, the relationship between the size of the blocks and the weighted density, and how the Cesàro–Stolz theorem can be applied to compute weighted densities. We also investigate the relationship between densities defined by the weight function f(n) and f∗(n) = f(n)/(f(1) + · · · + f(n)) in the case of block-structured sets.

Actions (login required)

Edit Item