A theorem on the average number of subfaces in arrangements and oriented matroids期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A theorem on the average number of subfaces in arrangements and oriented matroids

Authors:	Komei Fukuda Akihisa Tamura Takeshi Tokuyama

Affiliation:	(1) Graduate School of Systems Management, The University of Tsukuba, 3-29-1 Otsuka, Bunkyo-ku, 112 Tokyo, Japan;(2) Department of Information Sciences, Tokyo Institute of Technology, 2-12-1 Oh-okayama, Meguro-ku, 152 Tokyo, Japan;(3) IBM Research, Tokyo Research Laboratory, 5-11 Sanbancho, Chiyoda-ku, 102 Tokyo, Japan

Abstract:	It is known that for simple arrangements in thed-dimensional Euclidean spaceR^dThe average number ofj-dimensional subfaces of ak-dimensional face is less than $2^{k - j} left( {begin{array}{*{20}c} k j end{array} } right)$ . In this paper, we show that this is also true for all arrangements inR^d and for all oriented matroids, and we give combinatorial proofs.

Keywords:
本文献已被 SpringerLink 等数据库收录！