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 |
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