2022/10/18 by Fang, Jin-Hui, Csaba Sándor, Sándor, Csaba
Computer Science · Decision Sciences · Mathematics · #11B13 #11B34 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Number Theory (math.NT) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2210.09680
openalex publication_date 2022/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Two sets A,B of nonnegative integers are called additive complements, if all sufficiently large integers can be expressed as the sum of two elements from A and B. We further call A,B perfect additive complements if every nonnegative integer can be uniquely expressed as the sum of two elements from A and B. Let A(x) be the counting function of A. In this paper, we focus on the function SX, where SX=\limsupx→∞\fracmax\A(x),B(x)\√(x) was introduced by Erdős and Freud in 1984. As a main result, we determine the value of SX for perfect additive complements and further fix the infimum. We also give the absolute lower bound of SX for additive complements.