Recursivity and geometry of the hypercube

It is a difficult theoretical and computational problem to describe explicitly the list of hyper-planes spanned by the vertices of the n-cube. In this paper we describe a procedure to generate hyper-planes of the n-cube from hyper-planes of the ( n − 1)-cube. Our main theorem says that starting with...

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2005-03, Vol.397, p.223-233
Main Author: da Silva, Ilda P.F.
Format: Article
Language:English
Subjects:
Algebra
Euclidean space
Exact sciences and technology
Hyper-planes
Linear and multilinear algebra, matrix theory
Linear equation
Mathematics
n-Cube
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:It is a difficult theoretical and computational problem to describe explicitly the list of hyper-planes spanned by the vertices of the n-cube. In this paper we describe a procedure to generate hyper-planes of the n-cube from hyper-planes of the ( n − 1)-cube. Our main theorem says that starting with the hyper-planes of the 1-cube and iterating this procedure we obtain the complete list of hyper-planes of the n-cube up till n = 6. For n = 7, with this procedure, not all the hyper-planes are obtained. An explicit description of the hyper-planes of the 7- cube is given, followed by a brief analysis of some further consequences of the results obtained.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2004.10.016