Citation
B. Aronov et al., AN INVARIANT PROPERTY OF BALLS IN ARRANGEMENTS OF HYPERPLANES, Discrete & computational geometry, 10(4), 1993, pp. 421-425
Citations number
7
Categorie Soggetti
Computer Sciences, Special Topics","Mathematics, Pure","Computer Applications & Cybernetics",Mathematics
Journal title
ISSN journal
01795376
Volume
10
Issue
4
Year of publication
1993
Pages
421 - 425
Database
ISI
SICI code
0179-5376(1993)10:4<421:AIPOBI>2.0.ZU;2-Q
Abstract
Let H be a collection of n hyperplanes in d-space in general position.
For each tuple of d + 1 hyperplanes of H consider the open ball inscr
ibed in the simplex that they form. Let B(k) denote the number of such
balls intersected by exactly k hyperplanes, for k = 0, 1, ..., n - d
- 1. We show that \B(k)\ = (n - k - 1/d).