Pitfalls in Vertical Arrangements
نویسندگان
چکیده
منابع مشابه
On Vertical Decomposition of Arrangements of Hyperplanes in Four Dimensions
We show that, for any collection H of n hyperplanes in < 4 , the combinato-rial complexity of the vertical decomposition of the arrangement A(H) of H is O(n 4 log n). The proof relies on properties of superimposed convex subdivisions of 3-space, and we also derive some other results concerning them.
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We prove tight and near-tight combinatorial complexity bounds for vertical decompositions of arrangements of hyperplanes and 3-simplices in four dimensions. In particular, we prove a tight upper bound of Θ(n) for the vertical decomposition of an arrangement of n hyperplanes in four dimensions, improving the best previously known bound [8] by a logarithmic factor. We also show that the complexit...
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ژورنال
عنوان ژورنال: SSRN Electronic Journal
سال: 2010
ISSN: 1556-5068
DOI: 10.2139/ssrn.1681494