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Hausdorff metric on faces of the n-cube

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Abstract

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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References

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    G. G. Ryabov

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  1. G. G. Ryabov
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Correspondence to G. G. Ryabov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 16, No. 1, pp. 151–155, 2010.

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Ryabov, G.G. Hausdorff metric on faces of the n-cube. J Math Sci 177, 619–622 (2011). https://doi.org/10.1007/s10958-011-0487-3

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  • DOI: https://doi.org/10.1007/s10958-011-0487-3

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