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The slimmest arrangements of hyperplanes: II. Basepointed geometric lattices and Euclidean arrangements

Published online by Cambridge University Press:  26 February 2010

Thomas Zaslavsky
Thomas Zaslavsky
Affiliation:
Department of Mathematics, The Ohio State University, Columbus, Ohio 43210, U.S.A.
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Abstract

We calculate the minimum numbers of k-dimensional flats and cells of any Euclidean d-arrangement of n hyperplanes. The bounds are obtained by calculating lower bounds for the values of the doubly indexed Whitney numbers of a basepointed geometric lattice of rank r with n points. Additional geometric results concern the minimum number of cells of a Euclidean or projective arrangement met by a subspace in general position and the minimum number of non-Radon partitions of a Euclidean point set. We include remarks on the relationship between Euclidean arrangements and basepointed geometric lattices and on the minimum numbers of cells of arrangements with a bounded region.

Type
Research Article
Information
Mathematika , Volume 28 , Issue 2 , December 1981 , pp. 169 - 190
Copyright
Copyright © University College London 1981

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