Authors: | Bárány, Imre Blagojević, Pavle Dimitrijević-Blagojević, Aleksandra |
Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Functions, Measures, and Equipartitioning Convex k-Fans | Journal: | Discrete and Computational Geometry | Volume: | 49 | Issue: | 2 | First page: | 382 | Last page: | 401 | Issue Date: | 1-Jan-2013 | Rank: | M22 | ISSN: | 0179-5376 | DOI: | 10.1007/s00454-012-9467-8 | Abstract: | A k-fan in the plane is a point x∈ℝ2 and k halflines starting from x. There are k angular sectors σ1,...,σk between consecutive halflines. The k-fan is convex if every sector is convex. A (nice) probability measure μ is equipartitioned by the k-fan if μ(σi)=1/k for every sector. One of our results: Given a nice probability measure μ and a continuous function f defined on sectors, there is a convex 5-fan equipartitioning μ with f(σ1)=f(σ2)=f(σ3). |
Keywords: | Convex k-fans | Equipartitions | Functions on sectors | Measures | Publisher: | Springer Link | Project: | European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC, Grant agreement no. 247029-SDModels Advanced Techniques of Cryptology, Image Processing and Computational Topology for Information Security |
Show full item record
SCOPUSTM
Citations
2
checked on Nov 18, 2024
Page view(s)
15
checked on Nov 19, 2024
Google ScholarTM
Check
Altmetric
Altmetric
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.