Work

Harmonic progressions in additive combinatorics: van der Waerden, Szemerédi, and Green–Tao analogs

Year: 2026

Type: article

Abstract: This paper studies counting, coloring, and density results on harmonic progressions. We first estimate the number of three-term harmonic progressions. Then, we prove a van der Waerden-type theorem for harmonic progressions, present a Sárközy-type result, and give a height analog of Szemerédi's theorem. Moreover, we give a proof for the harmonic analog of Szemerédi's theorem for multiplicatively closed sets, and we prove the shifted versions of the Green–Tao and Szemerédi theorems for harmonic progressions.

Source: Discrete Mathematics

DOI: 10.1016/j.disc.2026.115425

Authors: Şermı̇n Çam Çelik, Haydar Göral, Doğa Can Sertbaş

Institutions: Izmir Institute of Technology, Yaşar University

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,320

Funder: Türkiye Bilimsel ve Teknolojik Araştırma Kurumu