On minimal Besicovitch arrangements

2018/05/15 by Stéphane Blondeau Da Silva, da Silva, Stéphane Blondeau
Computer Science · Engineering · Mathematics · #Advanced Combinatorial Mathematics #Cellular Automata and Applications #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Probability (math.PR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1805.05626

openalex publication_date 2018/05/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we focus on minimal Besicovitch arrangements to highlight some of their properties. An appropriate probability space enables us to find again in an elegant way some straightforward equalities associated with these arrangements. Resulting inequalities are also brought out. A connection with arrangements of lines in R2 is eventually made, where possible.

Related

• An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension
• On combinatorics of plus-one generated line arrangements
• On some freeness-type properties for line arrangements
• The intersection of typical Besicovitch sets with lines
• Complexities of Erez self-dual normal bases