Authors: Žunić, Joviša 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Cutting Corners by Circles and Spheres
Journal: Electronic Notes in Discrete Mathematics
Volume: 12
First page: 232
Last page: 242
Issue Date: 1-Jan-2003
ISSN: 1571-0653
DOI: 10.1016/S1571-0653(04)00489-5
Abstract: 
A circle corner cut A ⊂ N o2 is a planar set of points with nonnegative integer coordinates which includes the origin and which can be separated from N o2 \ A by a circle. In this paper we show that there are O(n 3 · log n) different circle corner cuts consisting of n points. If a sphere corner cut is defined as a set A ⊂ N o3 of points with nonnegative integer coordinates which includes the origin and which can be separated from N o3 \ A by a sphere, then there are O(n 4 · (log n) 2 ) different sphere corner cuts consisting of n points.
Keywords: Corner cuts | discrete moments | integer grid. | partitions
Publisher: Elsevier

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