Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
We study certain structural problems of arrangements of hyperplanes in d-dimensional Euclidean space. Of special interest are nontrivial relations satisfied by the f-vector f=(f0,f1,...,fd) of an arrangement, where fk denotes the number of k-faces. The first result is that the mean number of (k-1)-faces lying on the boundary of a fixed k-face is less than 2k in any arrangement, which implies the simple linear inequality fk>(d-k+1) kf--1 if fk≠0. Similar results hold for spherical arrangements and oriented matroids. We also show that the f-vector and the h-vector of a simple arrangement is logarithmic concave, and hence unimodal. © 1991.
Mario Blaum, John L. Fan, et al.
IEEE International Symposium on Information Theory - Proceedings
A.R. Conn, Nick Gould, et al.
Mathematics of Computation
A. Grill, B.S. Meyerson, et al.
Proceedings of SPIE 1989
A.R. Gourlay, G. Kaye, et al.
Proceedings of SPIE 1989