Density of integral sets with missing differences

2012/12/02 by Quan-Hui Yang, Min Tang, Yang, Quan-Hui +1
Mathematics · #11B05 #Advanced Topology and Set Theory #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT) #math.CO #math.NT #msc:11B05

paper · pdf · doi:10.48550/arxiv.1212.0209

9 pages, to appear in Ars Combinatoria

openalex publication_date 2012/12/02 · arxiv created 2013/08/28 · arxiv updated 2013/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motzkin posed the problem of finding the maximal density μ(M) of sets of integers in which the differences given by a set M do not occur. The problem is already settled when |M|≤ 2 and M is a finite arithmetic progression. In this paper, we determine μ(M) when M has some other structure. For example, we determine μ(M) when M is a finite geometric progression.

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