On Zones of Flats in Hyperplane Arrangements
نویسندگان
چکیده
Let H be a set of n hyperplanes in R d , let A(H) be its arrangement, and let b be an m-dimensional at. The zone of b in the arrangement A(H) is the set of open d-dimensional cells of A(H) which are intersected by b. We prove that the maximum number of incidences of k-cofaces of the arrangement with cells of the zone is O(n minfk+m;b d+m 2 cg k;d;m (n)), where k;d;m (n) = log n ifm 1, d+m is odd, d m 3 and k d d m 2 e; otherwise, k;d;m (n) = 1. A constructive lower bound of (n minfk+m;b d+m 2 cg ) is also shown. The bounds apply equally well to pseudo-arrangements and zones of pseudoats.
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