On compact packings of Euclidean space with spheres of finitely many sizes

2023/05/01 by Eder Kikianty, Kikianty, Eder, Miek Messerschmidt +1 · 1 citation
Computer Science · Mathematics · #05B40. Secondary: 57Q05 #52C26 #Combinatorics (math.CO) #Digital Image Processing Techniques #FOS: Mathematics #Metric Geometry (math.MG) #Point processes and geometric inequalities #Primary: 52C17 #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2305.00758

openalex publication_date 2023/05/01 · openalex created_date 2023/05/03 · openalex updated_date 2026/07/28

Abstract

For d∈ℕ, a compact sphere packing of Euclidean space ℝ^d is a set of spheres in ℝ^d with disjoint interiors so that the contact hypergraph of the packing is the vertex scheme of a homogeneous simplicial d-complex that covers all of ℝ^d. We are motivated by the question: For d,n∈ℕ with d,n≥2, how many configurations of numbers 0

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