2022/11/29 by Illya Ivanov, Ivanov, Illya, Cameron Strachan +1
Computer Science · Mathematics · #Combinatorics (math.CO) #Commutative Algebra and Its Applications #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric Topology (math.GT) #Point processes and geometric inequalities
paper · pdf · doi:10.48550/arxiv.2211.16621
openalex publication_date 2022/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a convex domain C, a C-polygon is an intersection of n≥ 2 homothets of C. If the homothets are translates of C then we call the intersection a translative C-polygon. This paper proves that if C is a strictly convex domain with m singular boundary points, then the number of singular boundary points a C-polygon has is between n and 2(n-1)+m. For a translative C-polygon we show the number of singular boundary points is between n and n+m.