Centre for Discrete and Applicable Mathematics

 CDAM Research Report, LSE-CDAM-2002-10

November 2002


Partitioning Points by Parallel Planes

Martin Anthony

Abstract

A new upper bound is given on the number of ways in which a set of N points in Rn can be partitioned by k parallel hyperplanes. This bound improves upon a result of Olafsson and Abu-Mostafa [IEEE Trans. Pattern Analysis and Machine Intelligence 10(2), 1988: 277-281]; it agrees with the known (tight) result for the case k = 1; and it is, for fixed k and n, tight to within a constant. A previously published claimed improvement to the bound of Olafsson and Abu-Mostafa is shown to be incorrect.


A PDF file (103 kB) with the full contents of this report can be downloaded by clicking here.

Alternatively, if you would like to get a free hard copy of this report, please send the number of this report, LSE-CDAM-2002-10, together with your name and postal address to:
CDAM Research Reports Series
Centre for Discrete and Applicable Mathematics
London School of Economics
Houghton Street
London WC2A 2AE, U.K.
Phone: +44(0)-20-7955 7732.
Fax: +44(0)-20-7955 6877.
Email: info@maths.lse.ac.uk


Introduction to the CDAM Research Report Series.
CDAM Homepage.


Copyright © London School of Economics & Political Science 2005

Last changed: Wed 9 Feb 2005
For comments go to: http://www.maths.lse.ac.uk/webmaster.html