2023/07/25 by Abdul Basit, Basit, Abdul, Alexander Clifton +3
Computer Science · #05D99 #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.2307.13257
openalex publication_date 2023/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Motivated by classical work of Alon and Füredi, we introduce and address the following problem: determine the minimum number of affine hyperplanes in ℝd needed to cover every point of the triangular grid Td(n) := \(x1,…,xd)∈ℤ≥ 0d| x1+…+xd≤ n-1\ at least k times. For d = 2, we solve the problem exactly for k ≤ 4, and obtain a partial solution for k > 4. We also obtain an asymptotic formula (in n) for all d ≥ k - 2. The proofs rely on combinatorial arguments and linear programming.