Avoiding intersections of given size in finite affine spaces AG(n,2)

2023/05/09 by Benedek Kovács, Zoltán Lóránt Nagy, Kovács, Benedek +1 · 2 citations
Computer Science · Engineering · Medicine · #Advanced Numerical Analysis Techniques #Chronic Lymphocytic Leukemia Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2305.05632

openalex publication_date 2023/05/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the set of intersection sizes of a k-dimensional affine subspace and a point set of size m ∈ [0, 2ⁿ] of the n-dimensional binary affine space AG(n,2). Following the theme of Erdős, Füredi, Rothschild and T. Sós, we partially determine which local densities in k-dimensional affine subspaces are unavoidable in all m-element point sets in the n-dimensional affine space. We also show constructions of point sets for which the intersection sizes with k-dimensional affine subspaces takes values from a set of a small size compared to 2^k. These are built up from affine subspaces and so-called subspace evasive sets. Meanwhile, we improve the best known upper bounds on subspace evasive sets and apply results concerning the canonical signed-digit (CSD) representation of numbers.

Cited by

• Cardinalities of the total number of independent sets
• Code-based [3,1]-avoiders in finite affine spaces AG(n,2)

Related

• Code-based [3,1]-avoiders in finite affine spaces AG(n,2)
• On Blocking Sets of Affine Spaces
• A new lower bound for the size of an affine blocking set
• Variety Evasive Sets
• Affine vector space partitions