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On Asymmetric Coverings and Covering Numbers by Applegate, David; Rains, E. M.; Sloane, N. J. A. is a scholarly article available to read on EtoBox.

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An asymmetric covering D(n,R) is a collection of special subsets S of an n-set such that every subset T of the n-set is contained in at least one special S with |S| - |T| <= R. In this paper we compute the smallest size of any D(n,1) for n <= 8. We also investigate ``continuous'' and ``banded'' versions of the problem. The latter involves the classical covering numbers C(n,k,k-1), and we determine the following new values: C(10,5,4) = 51, C(11,7,6,) =84, C(12,8,7) = 126, C(13,9,8)= 185 and C(14,10,9) = 259. We also find the number of nonisomorphic minimal covering designs in several cases.

Author

Applegate, David; Rains, E. M.; Sloane, N. J. A.

Published

2002

Language

EN