FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 1, PAGES 151-155

**Hausdorff metric on faces of the $n$-cube**

G. G. Ryabov

Abstract

View as HTML
View as gif image

The Hausdorff metric on all faces of the unit $n$-cube ($In$) is
considered.
The notion of a cubant is used; it was introduced as an
$n$-digit
quaternary code of a $k$-dimensional face
containing the Cartesian product of $k$ frame unit segments
and the face translation code within $In$.
The cubants form a semigroup with a unit (monoid) with
respect to the given operation of multiplication.
A calculation of Hausdorff metric based on the generalization of the
Hamming metric for binary codes is considered.
The supercomputing issues are discussed.

Location: http://mech.math.msu.su/~fpm/eng/k10/k101/k10112h.htm

Last modified: March 11, 2011