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

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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.

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Last modified: March 11, 2011