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- W2963669366 abstract "We study nested partitions of R d obtained by successive cuts using hyperplanes with fixed directions. We establish the number of measures that can be split evenly simultaneously by taking a partition of this kind and then distributing the parts among k sets. This generalises classical necklace splitting results and their more recent high-dimensional versions. With similar methods we show that in the plane, for any t measures there is a path formed only by horizontal and vertical segments using at most t - 1 turns that splits them by half simultaneously, and optimal masspartitioning results for chessboard colourings of R d using hyperplanes with fixed directions." @default.
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- W2963669366 date "2016-05-01" @default.
- W2963669366 modified "2023-09-30" @default.
- W2963669366 title "Measure partitions using hyperplanes with fixed directions" @default.
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- W2963669366 doi "https://doi.org/10.1007/s11856-016-1303-z" @default.
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