The slimmest arrangements of hyperplanes. I: Geometric lattices and projective arrangements
type: Item
instance of: scholarly article
title: The slimmest arrangements of hyperplanes. I: Geometric lattices and projective arrangements
zbMATH Open document ID: 0537.05017
DOI: 10.1007/BF00146905
author: Thomas Zaslavsky
published in: Geometriae Dedicata
publication date: 1983-01-01T00:00:00Z
review text: [For part II see Mathematika 28, 169-179 (1981; Zbl 0483.51012).] A projective d-arrangement of hyperplanes in real projective d-space is a finite set of hyperplanes, whose intersection is empty, and the resulting cell-complex decomposition of the space. The author is concerned with the establishment and characterization of lower bounds for the numbers of k- dimensional cells and k-dimensional flats in the d-arrangement \((0<k\leq d)\). Generalizations of Whitney numbers in a geometric lattice are used to this end.
Mathematics Subject Classification ID: 05B35
Mathematics Subject Classification ID: 05B30
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 3853095
zbMATH Keywords: projective arrangement
zbMATH Keywords: real projective space
zbMATH Keywords: Whitney numbers
zbMATH Keywords: geometric lattice
reviewed by: F. A. Sherk
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3853095