Hausdorff metric on faces of the <Emphasis Type="Italic">n</Emphasis>-cube |
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Authors: | G G Ryabov |
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Institution: | 1.Moscow State University,Moscow,Russia |
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Abstract: | The Hausdorff metric on all faces of the unit n-cube (I
n
) 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 I
n
. 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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Keywords: | |
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