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- W2017345057 abstract "Abstract Let H be a collection of n hyperplanes in R d, d⩾2. For each cell c of the arrangement of H let fi(c) denote the number of faces of c of dimension i, and let f(c) = ∑i=0d−1 fi(c). We prove that ∑ c f(c) 2 = O(n d log d 2 −1 n) , where the sum extends over all cells of the arrangement. Among other applications, we show that the total number of faces bounding any m distinct cells in an arrangement of n hyperplanes in R d is O(m 1 2 n d 2 log ( d 2 −1) 2 n) and provide a lower bound on the maximum possible face count in m distinct cells, which is close to the upper bound, and for many values of m and n is Ω(m 1 2 n d 2 ) ." @default.
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- W2017345057 date "1991-01-01" @default.
- W2017345057 modified "2023-09-24" @default.
- W2017345057 title "On the sum of squares of cell complexities in hyperplane arrangements" @default.
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- W2017345057 doi "https://doi.org/10.1145/109648.109682" @default.
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