Shape of the asymptotic maximum sum-free sets in integer lattice grids

2021/08/24 by Hong Liu, Guanghui Wang, Liu, Hong +4 · 2 citations
Computer Science · Mathematics · #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2108.10526

openalex publication_date 2021/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the shape of all sum-free sets in \1,2,…,n\² of size close to the maximum (3)/(5)n², solving a problem of Elsholtz and Rackham. We show that all such asymptotic maximum sum-free sets lie completely in the stripe (4)/(5)n-o(n)≤ x+y≤(8)/(5)n+ o(n). We also determine for any positive integer p the maximum size of a subset A⊆ \1,2,…,n\² which forbids the triple (x,y,z) satisfying px+py=z.

Citations

• On Certain Sets of Integers

Cited by

• On the number of sum-free subsets of the square grid
• Enumeration of subsets with closedness in finite fields of characteristic 2

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