BOUNDING THE NUMBER OF K-FACES IN ARRANGEMENTS OF HYPERPLANES

被引：11

作者：

FUKUDA, K

SAITO, S

TAMURA, A

TOKUYAMA, T

机构：

[1] TOKYO INST TECHNOL, DEPT INFORMAT SCI, MEGURO KU, TOKYO 152, JAPAN

[2] IBM CORP, RES, TOKYO RES LAB, CHIYODA KU, TOKYO 102, JAPAN

来源：

DISCRETE APPLIED MATHEMATICS | 1991年 / 31卷 / 02期

关键词：

D O I：

10.1016/0166-218X(91)90067-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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, ..., f(d)) of an arrangement, where f(k) 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 f(k) > (d - k + 1)/kf(k - 1) if f(k) not-equal 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.

引用

页码：151 / 165

页数：15